Best Known (64−38, 64, s)-Nets in Base 128
(64−38, 64, 384)-Net over F128 — Constructive and digital
Digital (26, 64, 384)-net over F128, using
- 2 times m-reduction [i] based on digital (26, 66, 384)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 23, 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, 43, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128 (see above)
- digital (3, 23, 192)-net over F128, using
- (u, u+v)-construction [i] based on
(64−38, 64, 407)-Net in Base 128 — Constructive
(26, 64, 407)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (1, 20, 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, 44, 257)-net in base 128, using
- 4 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
- 4 times m-reduction [i] based on (6, 48, 257)-net in base 128, using
- digital (1, 20, 150)-net over F128, using
(64−38, 64, 533)-Net over F128 — Digital
Digital (26, 64, 533)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12864, 533, F128, 38) (dual of [533, 469, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(12864, 536, F128, 38) (dual of [536, 472, 39]-code), using
- 21 step Varšamov–Edel lengthening with (ri) = (2, 20 times 0) [i] based on linear OA(12862, 513, F128, 38) (dual of [513, 451, 39]-code), using
- extended algebraic-geometric code AGe(F,474P) [i] based on function field F/F128 with g(F) = 24 and N(F) ≥ 513, using
- 21 step Varšamov–Edel lengthening with (ri) = (2, 20 times 0) [i] based on linear OA(12862, 513, F128, 38) (dual of [513, 451, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(12864, 536, F128, 38) (dual of [536, 472, 39]-code), using
(64−38, 64, 782306)-Net in Base 128 — Upper bound on s
There is no (26, 64, 782307)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 726 841462 417498 178848 432582 293205 075185 650237 963108 651964 793715 464870 756385 376470 402661 286162 142540 164400 250836 266200 716324 503957 911712 > 12864 [i]