Best Known (10, 47, s)-Nets in Base 128
(10, 47, 288)-Net over F128 — Constructive and digital
Digital (10, 47, 288)-net over F128, using
- t-expansion [i] based on digital (9, 47, 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
(10, 47, 296)-Net over F128 — Digital
Digital (10, 47, 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
(10, 47, 321)-Net in Base 128
(10, 47, 321)-net in base 128, using
- 17 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
(10, 47, 14426)-Net in Base 128 — Upper bound on s
There is no (10, 47, 14427)-net in base 128, because
- 1 times m-reduction [i] would yield (10, 46, 14427)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 8 550177 250526 442422 517788 206760 178847 677702 920875 689226 561654 285515 443781 651805 320715 268632 875127 > 12846 [i]