# eps_designs.py, D12 (one class), N = 3..6, EPSMAX = 1/2; solver status 0 = optimal. D12 is trivial (Prop. 9.11).
# commands: python3 eps_designs.py D12 N - MODE 600 - 1/2
== D12 N=3 - [nocopy] (coefficient cap 0.875, eps <= 0.5): status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.25000199999999995, 0.0s
  eps = 0.25000000
  tf: [1.0, 0.0] at [(1, 1, -1), (1, -1, 1)]
  R0 -0.25  Ra [0.125, -0.125, -0.25]
  pair (0,1) law P+(++)=1/10 P-(++)=7/22  coef -0.250000
  pair (0,2) law P+(++)=3/10 P-(++)=5/22  coef 0.250000
  rho_+: {'++-': 0.1, '+-+': 0.3, '-+-': 0.3, '--+': 0.1, '---': 0.2}
  rho_-: {'++-': 0.31818, '+-+': 0.22727, '-++': 0.09091, '-+-': 0.13636, '--+': 0.22727}
  max R 0.25  vertices at max: ['+-+', '+--', '-+-']
== D12 N=3 - [copy] (coefficient cap 0.875, eps <= 0.5): status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.250004, 0.0s
  eps = 0.25000000
  tf: [0.0, 0.0] at [(1, 1, -1), (1, -1, 1)]
  R0 -0.375  Ra [-0.25, -0.25, 0.125]
  pair (0,1) law P+(++)=1/10 P-(++)=7/22  coef -0.625000
  pair (0,2) law P+(++)=1/10 P-(++)=7/22  coef 0.375000
  pair (1,2) law P+(++)=3/10 P-(++)=5/22  coef 0.375000
  copy (0, 1, 2) pair laws [(0, 1, '1/10'), (0, 2, '1/10'), (1, 2, '3/10')]  coef 0.125000
  rho_+: {'+++': 0.1, '+--': 0.3, '-++': 0.2, '-+-': 0.1, '--+': 0.1, '---': 0.2}
  rho_-: {'+++': 0.13636, '++-': 0.18182, '+-+': 0.18182, '+--': 0.04545, '-++': 0.09091, '-+-': 0.13636, '--+': 0.13636, '---': 0.09091}
  max R 0.25  vertices at max: ['+-+', '+--', '-++', '-+-']
== D12 N=4 - [nocopy] (coefficient cap 0.875, eps <= 0.5): status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.08333733333332449, 0.1s
  eps = 0.08333333
  tf: [1.0, 0.0] at [(1, 1, -1), (1, -1, 1)]
  R0 -0.25  Ra [-0.0, -0.0, -0.125, -0.125]
  pair (0,1) law P+(++)=3/10 P-(++)=5/22  coef 0.083333
  pair (0,3) law P+(++)=3/10 P-(++)=5/22  coef 0.083333
  pair (1,2) law P+(++)=3/10 P-(++)=5/22  coef 0.083333
  pair (2,3) law P+(++)=1/10 P-(++)=7/22  coef -0.250000
  rho_+: {'++++': 0.1, '+++-': 0.1, '++-+': 0.1, '+--+': 0.1, '-++-': 0.1, '--+-': 0.1, '---+': 0.1, '----': 0.3}
  rho_-: {'++++': 0.13636, '++--': 0.09091, '+-++': 0.09091, '+-+-': 0.22727, '-+++': 0.09091, '-+-+': 0.09091, '-+--': 0.13636, '---+': 0.13636}
  max R 0.08333333  vertices at max: ['+++-', '++-+', '+--+', '-++-', '--+-', '---+']
== D12 N=4 - [copy] (coefficient cap 0.875, eps <= 0.5): status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.16667266666666603, 0.0s
  eps = 0.16666667
  tf: [0.0, 0.0] at [(1, 1, -1), (1, -1, 1)]
  R0 -0.375  Ra [-0.25, -0.25, 0.125, -0.0]
  pair (0,1) law P+(++)=1/10 P-(++)=7/22  coef -0.500000
  pair (0,2) law P+(++)=1/10 P-(++)=7/22  coef 0.333333
  pair (0,3) law P+(++)=1/10 P-(++)=7/22  coef -0.041667
  pair (1,2) law P+(++)=3/10 P-(++)=5/22  coef 0.375000
  pair (2,3) law P+(++)=1/10 P-(++)=7/22  coef -0.041667
  copy (0, 1, 2) pair laws [(0, 1, '1/10'), (0, 2, '1/10'), (1, 2, '3/10')]  coef 0.125000
  rho_+: {'++++': 0.1, '+---': 0.3, '-++-': 0.2, '-+-+': 0.1, '--+-': 0.1, '---+': 0.2}
  rho_-: {'++++': 0.04545, '+++-': 0.09091, '++-+': 0.04545, '++--': 0.13636, '+-++': 0.18182, '+--+': 0.04545, '-+++': 0.09091, '-+-+': 0.13636, '--+-': 0.13636, '----': 0.09091}
  max R 0.16666667  vertices at max: ['+-+-', '+--+', '+---', '-+++', '-++-', '-+-+', '---+']
== D12 N=5 - [nocopy] (coefficient cap 0.875, eps <= 0.5): status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.05556155555555484, 1.1s
  eps = 0.05555556
  tf: [1.0, 0.0] at [(1, 1, -1), (1, -1, 1)]
  R0 -0.25  Ra [-0.125, -0.0, -0.125, -0.0, -0.0]
  pair (0,1) law P+(++)=1/10 P-(++)=7/22  coef -0.097222
  pair (0,2) law P+(++)=1/10 P-(++)=7/22  coef -0.138889
  pair (0,3) law P+(++)=3/10 P-(++)=5/22  coef 0.083333
  pair (1,2) law P+(++)=1/10 P-(++)=7/22  coef -0.013889
  pair (1,4) law P+(++)=3/10 P-(++)=5/22  coef 0.083333
  pair (3,4) law P+(++)=3/10 P-(++)=5/22  coef 0.083333
  rho_+: {'++-++': 0.1, '+-++-': 0.1, '+--++': 0.1, '+----': 0.1, '-++++': 0.1, '-+--+': 0.1, '-+---': 0.1, '--+--': 0.2, '-----': 0.1}
  rho_-: {'++++-': 0.18182, '++--+': 0.04545, '++---': 0.09091, '+-+-+': 0.13636, '+--++': 0.04545, '+----': 0.04545, '-++++': 0.09091, '-+++-': 0.04545, '-+-++': 0.09091, '--++-': 0.09091, '----+': 0.13636}
  max R 0.05555556  vertices at max: ['++-++', '+--++', '+--+-', '+----', '-++++', '-++-+', '-++--', '-+-++', '-+--+', '-+---', '--+--']
== D12 N=5 - [copy] (coefficient cap 0.875, eps <= 0.5): status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.05556355555555178, 0.2s
  eps = 0.05555556
  tf: [0.0, 1.0] at [(1, 1, -1), (1, -1, 1)]
  R0 -0.25  Ra [-0.0, -0.125, -0.0, -0.125, -0.0]
  pair (0,1) law P+(++)=1/10 P-(++)=7/22  coef -0.013889
  pair (0,2) law P+(++)=1/10 P-(++)=7/22  coef -0.000000
  pair (0,3) law P+(++)=1/10 P-(++)=7/22  coef -0.013889
  pair (1,2) law P+(++)=3/10 P-(++)=5/22  coef 0.083333
  pair (1,3) law P+(++)=1/10 P-(++)=7/22  coef -0.222222
  pair (2,4) law P+(++)=3/10 P-(++)=5/22  coef 0.083333
  pair (3,4) law P+(++)=3/10 P-(++)=5/22  coef 0.083333
  copy (0, 1, 2) pair laws [(0, 1, '1/10'), (0, 2, '1/10'), (1, 2, '3/10')]  coef -0.000000
  rho_+: {'+++--': 0.1, '+--++': 0.1, '+----': 0.2, '-++++': 0.1, '-++-+': 0.1, '-+---': 0.1, '--+++': 0.1, '---+-': 0.1, '-----': 0.1}
  rho_-: {'++++-': 0.13636, '++-+-': 0.02273, '++--+': 0.15909, '+-+++': 0.15909, '+-+-+': 0.02273, '+---+': 0.04545, '-+++-': 0.09091, '-+-++': 0.06818, '-+---': 0.06818, '--++-': 0.02273, '--+-+': 0.04545, '--+--': 0.06818, '---+-': 0.04545, '----+': 0.04545}
  max R 0.05555556  vertices at max: ['+++-+', '+++--', '++---', '+-+++', '+--++', '+--+-', '+----', '-++-+', '-++--', '-+---', '--+++', '---++', '---+-']
== D12 N=6 - [nocopy] (coefficient cap 0.875, eps <= 0.5): status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.03333944761904762, 94.5s
  eps = 0.03333333
  tf: [1.0, 0.0] at [(1, 1, -1), (1, -1, 1)]
  R0 -0.25  Ra [0.05, -0.05, -0.125, -0.125, -0.0, -0.0]
  pair (0,2) law P+(++)=3/10 P-(++)=5/22  coef 0.050000
  pair (0,4) law P+(++)=3/10 P-(++)=5/22  coef 0.050000
  pair (0,5) law P+(++)=3/10 P-(++)=5/22  coef 0.050000
  pair (1,2) law P+(++)=1/10 P-(++)=7/22  coef -0.058333
  pair (1,3) law P+(++)=1/10 P-(++)=7/22  coef -0.058333
  pair (1,5) law P+(++)=3/10 P-(++)=5/22  coef 0.050000
  pair (2,3) law P+(++)=1/10 P-(++)=7/22  coef -0.133333
  pair (3,4) law P+(++)=3/10 P-(++)=5/22  coef 0.050000
  rho_+: {'+++-++': 0.1, '++-+++': 0.1, '+-++++': 0.1, '+-+---': 0.1, '-+---+': 0.1, '-+----': 0.1, '--+---': 0.1, '---++-': 0.1, '---+--': 0.1, '------': 0.1}
  rho_-: {'++++--': 0.13636, '+++-+-': 0.09091, '++-+-+': 0.04545, '++--++': 0.04545, '+--+--': 0.09091, '+---++': 0.09091, '+----+': 0.04545, '-+++-+': 0.04545, '-++-+-': 0.04545, '-+-+++': 0.09091, '-+--+-': 0.04545, '--++++': 0.13636, '--+--+': 0.04545, '--+---': 0.04545}
  max R 0.03333333  vertices at max: ['+++-++', '+++--+', '++-+++', '++--++', '++---+', '+-+-++', '+-+-+-', '+-+--+', '+-+---', '+--+++', '+--++-', '-+---+', '-+----', '--+---', '---++-', '---+--']
== D12 N=6 - [copy] (coefficient cap 0.875, eps <= 0.5): status 0 (Optimization terminated successfully. (HiGHS Status 7: Optim), dual bound 0.033343333333333294, 7.4s
  eps = 0.03333333
  tf: [0.0, 1.5] at [(1, 1, -1), (1, -1, 1)]
  R0 -0.1875  Ra [-0.0625, -0.0625, -0.0625, -0.05, 0.05, -0.0]
  pair (0,1) law P+(++)=1/10 P-(++)=7/22  coef -0.062500
  pair (0,2) law P+(++)=1/10 P-(++)=7/22  coef -0.070833
  pair (0,3) law P+(++)=1/10 P-(++)=7/22  coef -0.058333
  pair (0,5) law P+(++)=3/10 P-(++)=5/22  coef 0.050000
  pair (1,2) law P+(++)=3/10 P-(++)=5/22  coef -0.012500
  pair (1,4) law P+(++)=3/10 P-(++)=5/22  coef 0.050000
  pair (2,3) law P+(++)=1/10 P-(++)=7/22  coef -0.058333
  pair (3,4) law P+(++)=3/10 P-(++)=5/22  coef 0.050000
  pair (4,5) law P+(++)=3/10 P-(++)=5/22  coef 0.050000
  copy (0, 1, 2) pair laws [(0, 1, '1/10'), (0, 2, '1/10'), (1, 2, '3/10')]  coef -0.062500
  rho_+: {'+++-++': 0.1, '+--+++': 0.1, '+----+': 0.1, '+-----': 0.1, '-+++++': 0.1, '-++---': 0.1, '-+-++-': 0.1, '--+---': 0.1, '---+--': 0.1, '------': 0.1}
  rho_-: {'++++--': 0.09091, '+++-+-': 0.04545, '++-+++': 0.04545, '++--++': 0.13636, '+-+++-': 0.13636, '+-+---': 0.04545, '+--+++': 0.04545, '-+++-+': 0.09091, '-+-+-+': 0.13636, '--+-+-': 0.13636, '-----+': 0.09091}
  max R 0.03333333  vertices at max: ['++-+++', '++--++', '+-+-++', '+-+--+', '+-+---', '+--+++', '+---++', '+----+', '+-----', '-+++++', '-++++-', '-++-++', '-++-+-', '-++---', '-+-+++', '-+-++-', '--+---', '---+++', '---++-', '---+--']
