Best Known (42−30, 42, s)-Nets in Base 128
(42−30, 42, 288)-Net over F128 — Constructive and digital
Digital (12, 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
(42−30, 42, 321)-Net over F128 — Digital
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
(42−30, 42, 40185)-Net in Base 128 — Upper bound on s
There is no (12, 42, 40186)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 31829 634492 888572 518477 880571 446464 626702 927159 085100 078369 274136 477272 242415 310940 326776 > 12842 [i]