Best Known (73−58, 73, s)-Nets in Base 64
(73−58, 73, 177)-Net over F64 — Constructive and digital
Digital (15, 73, 177)-net over F64, using
- t-expansion [i] based on digital (7, 73, 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
(73−58, 73, 192)-Net in Base 64 — Constructive
(15, 73, 192)-net in base 64, using
- 11 times m-reduction [i] based on (15, 84, 192)-net in base 64, using
- base change [i] based on digital (3, 72, 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
- base change [i] based on digital (3, 72, 192)-net over F128, using
(73−58, 73, 258)-Net over F64 — Digital
Digital (15, 73, 258)-net over F64, using
- net from sequence [i] based on digital (15, 257)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 15 and N(F) ≥ 258, using
(73−58, 73, 6507)-Net in Base 64 — Upper bound on s
There is no (15, 73, 6508)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 711634 079034 204074 823139 666263 376611 266966 012961 214229 050795 227118 928273 105433 423022 141866 067080 922833 580252 518352 810245 046140 006184 > 6473 [i]