Best Known (7, 7+11, s)-Nets in Base 64
(7, 7+11, 177)-Net over F64 — Constructive and digital
Digital (7, 18, 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
(7, 7+11, 259)-Net in Base 64 — Constructive
(7, 18, 259)-net in base 64, using
- 2 times m-reduction [i] based on (7, 20, 259)-net in base 64, using
- base change [i] based on digital (2, 15, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- base change [i] based on digital (2, 15, 259)-net over F256, using
(7, 7+11, 321)-Net in Base 64
(7, 18, 321)-net in base 64, using
- 2 times m-reduction [i] based on (7, 20, 321)-net in base 64, using
- base change [i] based on digital (2, 15, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 15, 321)-net over F256, using
(7, 7+11, 57212)-Net in Base 64 — Upper bound on s
There is no (7, 18, 57213)-net in base 64, because
- 1 times m-reduction [i] would yield (7, 17, 57213)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 5 070771 304122 500904 786672 325240 > 6417 [i]