Best Known (73−47, 73, s)-Nets in Base 128
(73−47, 73, 321)-Net over F128 — Constructive and digital
Digital (26, 73, 321)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 23, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (3, 50, 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 (0, 23, 129)-net over F128, using
(73−47, 73, 513)-Net over F128 — Digital
Digital (26, 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
(73−47, 73, 293169)-Net in Base 128 — Upper bound on s
There is no (26, 73, 293170)-net in base 128, because
- 1 times m-reduction [i] would yield (26, 72, 293170)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 52 374660 759480 021157 173854 113259 239739 108570 370529 176831 192763 146511 575562 136894 006535 238228 469622 061763 683283 297460 065165 439325 100299 009244 336468 527728 > 12872 [i]