Best Known (92−49, 92, s)-Nets in Base 16
(92−49, 92, 225)-Net over F16 — Constructive and digital
Digital (43, 92, 225)-net over F16, using
- t-expansion [i] based on digital (40, 92, 225)-net over F16, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 40 and N(F) ≥ 225, using
- net from sequence [i] based on digital (40, 224)-sequence over F16, using
(92−49, 92, 244)-Net over F16 — Digital
Digital (43, 92, 244)-net over F16, using
(92−49, 92, 257)-Net in Base 16
(43, 92, 257)-net in base 16, using
- 1 times m-reduction [i] based on (43, 93, 257)-net in base 16, using
- base change [i] based on digital (12, 62, 257)-net over F64, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 12 and N(F) ≥ 257, using
- net from sequence [i] based on digital (12, 256)-sequence over F64, using
- base change [i] based on digital (12, 62, 257)-net over F64, using
(92−49, 92, 24024)-Net in Base 16 — Upper bound on s
There is no (43, 92, 24025)-net in base 16, because
- 1 times m-reduction [i] would yield (43, 91, 24025)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 37 591275 503517 788956 704016 103385 055065 028186 877818 019135 793625 084578 191109 804947 339720 006618 744626 339392 331501 > 1691 [i]