Best Known (101−55, 101, s)-Nets in Base 16
(101−55, 101, 225)-Net over F16 — Constructive and digital
Digital (46, 101, 225)-net over F16, using
- t-expansion [i] based on digital (40, 101, 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
(101−55, 101, 243)-Net over F16 — Digital
Digital (46, 101, 243)-net over F16, using
- net from sequence [i] based on digital (46, 242)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 46 and N(F) ≥ 243, using
(101−55, 101, 257)-Net in Base 16
(46, 101, 257)-net in base 16, using
- 1 times m-reduction [i] based on (46, 102, 257)-net in base 16, using
- base change [i] based on digital (12, 68, 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, 68, 257)-net over F64, using
(101−55, 101, 20975)-Net in Base 16 — Upper bound on s
There is no (46, 101, 20976)-net in base 16, because
- 1 times m-reduction [i] would yield (46, 100, 20976)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 2 583821 342743 331517 621128 837980 779795 077765 967876 478211 095978 518983 959630 053917 282325 160209 247857 238404 899643 257310 845506 > 16100 [i]