Best Known (59−49, 59, s)-Nets in Base 128
(59−49, 59, 288)-Net over F128 — Constructive and digital
Digital (10, 59, 288)-net over F128, using
- t-expansion [i] based on digital (9, 59, 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
(59−49, 59, 296)-Net over F128 — Digital
Digital (10, 59, 296)-net over F128, using
- net from sequence [i] based on digital (10, 295)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 10 and N(F) ≥ 296, using
(59−49, 59, 321)-Net in Base 128
(10, 59, 321)-net in base 128, using
- 5 times m-reduction [i] based on (10, 64, 321)-net in base 128, using
- base change [i] based on digital (2, 56, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 56, 321)-net over F256, using
(59−49, 59, 9537)-Net in Base 128 — Upper bound on s
There is no (10, 59, 9538)-net in base 128, because
- 1 times m-reduction [i] would yield (10, 58, 9538)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 165 318744 819687 896730 306086 593200 942107 114135 170636 881425 043681 490383 454922 956520 533987 337320 050463 574551 150777 560761 607976 > 12858 [i]