Best Known (95−51, 95, s)-Nets in Base 16
(95−51, 95, 225)-Net over F16 — Constructive and digital
Digital (44, 95, 225)-net over F16, using
- t-expansion [i] based on digital (40, 95, 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
(95−51, 95, 241)-Net over F16 — Digital
Digital (44, 95, 241)-net over F16, using
(95−51, 95, 257)-Net in Base 16
(44, 95, 257)-net in base 16, using
- 1 times m-reduction [i] based on (44, 96, 257)-net in base 16, using
- base change [i] based on digital (12, 64, 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, 64, 257)-net over F64, using
(95−51, 95, 22843)-Net in Base 16 — Upper bound on s
There is no (44, 95, 22844)-net in base 16, because
- 1 times m-reduction [i] would yield (44, 94, 22844)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 153968 610985 860153 537853 459152 120103 841860 962565 467474 248473 023850 185135 532814 871604 454642 758292 343699 182806 610251 > 1694 [i]