Best Known (42−29, 42, s)-Nets in Base 128
(42−29, 42, 288)-Net over F128 — Constructive and digital
Digital (13, 42, 288)-net over F128, using
- t-expansion [i] based on digital (9, 42, 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
(42−29, 42, 321)-Net over F128 — Digital
Digital (13, 42, 321)-net over F128, using
- t-expansion [i] based on digital (12, 42, 321)-net over F128, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 12 and N(F) ≥ 321, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
(42−29, 42, 70587)-Net in Base 128 — Upper bound on s
There is no (13, 42, 70588)-net in base 128, because
- 1 times m-reduction [i] would yield (13, 41, 70588)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 248 682575 886138 764023 451051 366125 898018 431049 763280 828907 733880 263938 551042 999587 641508 > 12841 [i]