Best Known (50, 113, s)-Nets in Base 16
(50, 113, 243)-Net over F16 — Constructive and digital
Digital (50, 113, 243)-net over F16, using
- t-expansion [i] based on digital (48, 113, 243)-net over F16, using
- net from sequence [i] based on digital (48, 242)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 48 and N(F) ≥ 243, using
- net from sequence [i] based on digital (48, 242)-sequence over F16, using
(50, 113, 255)-Net over F16 — Digital
Digital (50, 113, 255)-net over F16, using
- net from sequence [i] based on digital (50, 254)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 50 and N(F) ≥ 255, using
(50, 113, 257)-Net in Base 16
(50, 113, 257)-net in base 16, using
- 1 times m-reduction [i] based on (50, 114, 257)-net in base 16, using
- base change [i] based on digital (12, 76, 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, 76, 257)-net over F64, using
(50, 113, 18531)-Net in Base 16 — Upper bound on s
There is no (50, 113, 18532)-net in base 16, because
- 1 times m-reduction [i] would yield (50, 112, 18532)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 727 425177 990328 629707 441793 658347 736153 933742 552187 862275 028629 764939 705767 552473 831950 183289 074270 531184 560695 852989 174820 060564 101256 > 16112 [i]