Best Known (88−68, 88, s)-Nets in Base 64
(88−68, 88, 177)-Net over F64 — Constructive and digital
Digital (20, 88, 177)-net over F64, using
- t-expansion [i] based on digital (7, 88, 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
(88−68, 88, 216)-Net in Base 64 — Constructive
(20, 88, 216)-net in base 64, using
- t-expansion [i] based on (18, 88, 216)-net in base 64, using
- 3 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
- 3 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
(88−68, 88, 342)-Net over F64 — Digital
Digital (20, 88, 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
(88−68, 88, 10144)-Net in Base 64 — Upper bound on s
There is no (20, 88, 10145)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 880 554102 072656 757132 872364 596184 585736 017621 606892 908704 863964 402638 045543 869500 529893 690958 625177 797001 368307 697717 144492 561491 218042 645795 246529 545883 170112 > 6488 [i]