Best Known (61−36, 61, s)-Nets in Base 128
(61−36, 61, 384)-Net over F128 — Constructive and digital
Digital (25, 61, 384)-net over F128, using
- 2 times m-reduction [i] based on digital (25, 63, 384)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 22, 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, 41, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128 (see above)
- digital (3, 22, 192)-net over F128, using
- (u, u+v)-construction [i] based on
(61−36, 61, 407)-Net in Base 128 — Constructive
(25, 61, 407)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (1, 19, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- (6, 42, 257)-net in base 128, using
- 6 times m-reduction [i] based on (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
- 6 times m-reduction [i] based on (6, 48, 257)-net in base 128, using
- digital (1, 19, 150)-net over F128, using
(61−36, 61, 536)-Net over F128 — Digital
Digital (25, 61, 536)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12861, 536, F128, 36) (dual of [536, 475, 37]-code), using
- 22 step Varšamov–Edel lengthening with (ri) = (1, 21 times 0) [i] based on linear OA(12860, 513, F128, 36) (dual of [513, 453, 37]-code), using
- extended algebraic-geometric code AGe(F,476P) [i] based on function field F/F128 with g(F) = 24 and N(F) ≥ 513, using
- 22 step Varšamov–Edel lengthening with (ri) = (1, 21 times 0) [i] based on linear OA(12860, 513, F128, 36) (dual of [513, 453, 37]-code), using
(61−36, 61, 823042)-Net in Base 128 — Upper bound on s
There is no (25, 61, 823043)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 346 587979 613504 281962 397291 674940 622771 560331 509472 897681 034726 792549 711297 699210 949013 664208 475872 412485 573678 176286 087225 951120 > 12861 [i]