Best Known (63−49, 63, s)-Nets in Base 128
(63−49, 63, 288)-Net over F128 — Constructive and digital
Digital (14, 63, 288)-net over F128, using
- t-expansion [i] based on digital (9, 63, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
(63−49, 63, 353)-Net over F128 — Digital
Digital (14, 63, 353)-net over F128, using
- net from sequence [i] based on digital (14, 352)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 14 and N(F) ≥ 353, using
(63−49, 63, 21426)-Net in Base 128 — Upper bound on s
There is no (14, 63, 21427)-net in base 128, because
- 1 times m-reduction [i] would yield (14, 62, 21427)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 44395 649086 688082 955117 122284 999186 576790 239780 289302 324872 929617 574082 100331 418726 528714 845331 266362 732433 777657 168017 064032 352572 > 12862 [i]