Best Known (13, 13+63, s)-Nets in Base 64
(13, 13+63, 177)-Net over F64 — Constructive and digital
Digital (13, 76, 177)-net over F64, using
- t-expansion [i] based on digital (7, 76, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
(13, 13+63, 257)-Net over F64 — Digital
Digital (13, 76, 257)-net over F64, using
- t-expansion [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
(13, 13+63, 4602)-Net in Base 64 — Upper bound on s
There is no (13, 76, 4603)-net in base 64, because
- 1 times m-reduction [i] would yield (13, 75, 4603)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 2910 794505 673007 982117 217583 161245 468956 241373 633962 485785 341792 124783 477353 331534 425105 139026 107213 213167 073190 438604 097025 124765 947040 > 6475 [i]