Best Known (91−75, 91, s)-Nets in Base 64
(91−75, 91, 177)-Net over F64 — Constructive and digital
Digital (16, 91, 177)-net over F64, using
- t-expansion [i] based on digital (7, 91, 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
(91−75, 91, 192)-Net in Base 64 — Constructive
(16, 91, 192)-net in base 64, using
- base change [i] based on digital (3, 78, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
(91−75, 91, 267)-Net over F64 — Digital
Digital (16, 91, 267)-net over F64, using
- net from sequence [i] based on digital (16, 266)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 16 and N(F) ≥ 267, using
(91−75, 91, 5735)-Net in Base 64 — Upper bound on s
There is no (16, 91, 5736)-net in base 64, because
- 1 times m-reduction [i] would yield (16, 90, 5736)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 3 608738 141939 989479 244511 686178 568261 151617 490897 893677 305584 683457 363235 653099 188819 036983 675405 660945 251192 048628 268222 800389 279614 807215 125098 346460 686877 095253 > 6490 [i]