Best Known (63−55, 63, s)-Nets in Base 128
(63−55, 63, 216)-Net over F128 — Constructive and digital
Digital (8, 63, 216)-net over F128, using
- t-expansion [i] based on digital (5, 63, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
(63−55, 63, 257)-Net in Base 128 — Constructive
(8, 63, 257)-net in base 128, using
- 1 times m-reduction [i] based on (8, 64, 257)-net in base 128, using
- base change [i] based on digital (0, 56, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 56, 257)-net over F256, using
(63−55, 63, 276)-Net over F128 — Digital
Digital (8, 63, 276)-net over F128, using
- net from sequence [i] based on digital (8, 275)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 8 and N(F) ≥ 276, using
(63−55, 63, 5921)-Net in Base 128 — Upper bound on s
There is no (8, 63, 5922)-net in base 128, because
- 1 times m-reduction [i] would yield (8, 62, 5922)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 44512 932868 348415 899201 496115 837850 722855 546457 793482 424204 473781 208265 336376 723038 365893 514067 545129 732920 993623 460197 249759 058960 > 12862 [i]