Best Known (111−61, 111, s)-Nets in Base 16
(111−61, 111, 243)-Net over F16 — Constructive and digital
Digital (50, 111, 243)-net over F16, using
- t-expansion [i] based on digital (48, 111, 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
(111−61, 111, 255)-Net over F16 — Digital
Digital (50, 111, 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
(111−61, 111, 257)-Net in Base 16
(50, 111, 257)-net in base 16, using
- 3 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
(111−61, 111, 20867)-Net in Base 16 — Upper bound on s
There is no (50, 111, 20868)-net in base 16, because
- 1 times m-reduction [i] would yield (50, 110, 20868)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 2 843139 179217 617352 635654 447897 667384 360251 011522 687983 664165 848866 244552 958069 878233 915482 202864 561332 596677 825770 964585 113021 770976 > 16110 [i]