Best Known (27, 27+42, s)-Nets in Base 128
(27, 27+42, 384)-Net over F128 — Constructive and digital
Digital (27, 69, 384)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 24, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (3, 45, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128 (see above)
- digital (3, 24, 192)-net over F128, using
(27, 27+42, 386)-Net in Base 128 — Constructive
(27, 69, 386)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 21, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- (6, 48, 257)-net in base 128, using
- base change [i] based on digital (0, 42, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 42, 257)-net over F256, using
- digital (0, 21, 129)-net over F128, using
(27, 27+42, 514)-Net over F128 — Digital
Digital (27, 69, 514)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(12869, 514, F128, 3, 42) (dual of [(514, 3), 1473, 43]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(12866, 513, F128, 3, 42) (dual of [(513, 3), 1473, 43]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,1496P) [i] based on function field F/F128 with g(F) = 24 and N(F) ≥ 513, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(12866, 513, F128, 3, 42) (dual of [(513, 3), 1473, 43]-NRT-code), using
(27, 27+42, 573285)-Net in Base 128 — Upper bound on s
There is no (27, 69, 573286)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 24 974339 003996 187339 410133 755291 592215 947046 384446 817568 816950 654485 194259 179323 145164 679498 378013 762367 869442 480984 703379 123580 348428 540971 256182 > 12869 [i]