Best Known (82−62, 82, s)-Nets in Base 64
(82−62, 82, 177)-Net over F64 — Constructive and digital
Digital (20, 82, 177)-net over F64, using
- t-expansion [i] based on digital (7, 82, 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
(82−62, 82, 216)-Net in Base 64 — Constructive
(20, 82, 216)-net in base 64, using
- t-expansion [i] based on (18, 82, 216)-net in base 64, using
- 9 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- base change [i] based on digital (5, 78, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 78, 216)-net over F128, using
- 9 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
(82−62, 82, 342)-Net over F64 — Digital
Digital (20, 82, 342)-net over F64, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
(82−62, 82, 11796)-Net in Base 64 — Upper bound on s
There is no (20, 82, 11797)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 12797 292708 120316 572612 768416 523585 789123 561993 111524 026184 379251 820845 600525 313244 625879 648249 937661 816568 679369 803100 801655 223968 956217 623661 003264 > 6482 [i]