Best Known (63−42, 63, s)-Nets in Base 64
(63−42, 63, 177)-Net over F64 — Constructive and digital
Digital (21, 63, 177)-net over F64, using
- t-expansion [i] based on digital (7, 63, 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
(63−42, 63, 288)-Net in Base 64 — Constructive
(21, 63, 288)-net in base 64, using
- 21 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- base change [i] based on digital (9, 72, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 72, 288)-net over F128, using
(63−42, 63, 342)-Net over F64 — Digital
Digital (21, 63, 342)-net over F64, using
- t-expansion [i] based on digital (20, 63, 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
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
(63−42, 63, 36105)-Net in Base 64 — Upper bound on s
There is no (21, 63, 36106)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 616004 920136 380231 691119 970668 875581 279943 996450 792084 520650 763919 979875 148637 171204 502311 723935 565589 489714 890336 > 6463 [i]