Best Known (27, 27+46, s)-Nets in Base 128
(27, 27+46, 342)-Net over F128 — Constructive and digital
Digital (27, 73, 342)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 24, 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
- digital (3, 49, 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 (1, 24, 150)-net over F128, using
(27, 27+46, 513)-Net over F128 — Digital
Digital (27, 73, 513)-net over F128, using
- t-expansion [i] based on digital (24, 73, 513)-net over F128, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 24 and N(F) ≥ 513, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
(27, 27+46, 362026)-Net in Base 128 — Upper bound on s
There is no (27, 73, 362027)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 6704 119715 104519 828151 173038 282833 331058 558086 014184 975170 470322 552993 054619 016303 011323 304660 630598 077040 350409 832272 990488 479486 888341 352356 843527 381296 > 12873 [i]