Best Known (20, 20+70, s)-Nets in Base 64
(20, 20+70, 177)-Net over F64 — Constructive and digital
Digital (20, 90, 177)-net over F64, using
- t-expansion [i] based on digital (7, 90, 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
(20, 20+70, 216)-Net in Base 64 — Constructive
(20, 90, 216)-net in base 64, using
- t-expansion [i] based on (18, 90, 216)-net in base 64, using
- 1 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
- 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
(20, 20+70, 342)-Net over F64 — Digital
Digital (20, 90, 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
(20, 20+70, 9718)-Net in Base 64 — Upper bound on s
There is no (20, 90, 9719)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 3 604657 336645 738859 467906 150634 183308 824861 433243 801398 799642 182360 257536 203321 823533 369264 112563 333608 938032 205042 190765 598741 918106 536543 621608 687849 061619 398220 > 6490 [i]