Best Known (26, 26+50, s)-Nets in Base 64
(26, 26+50, 177)-Net over F64 — Constructive and digital
Digital (26, 76, 177)-net over F64, using
- t-expansion [i] based on digital (7, 76, 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
(26, 26+50, 288)-Net in Base 64 — Constructive
(26, 76, 288)-net in base 64, using
- t-expansion [i] based on (22, 76, 288)-net in base 64, using
- 15 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 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, 78, 288)-net over F128, using
- 15 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
(26, 26+50, 425)-Net over F64 — Digital
Digital (26, 76, 425)-net over F64, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 26 and N(F) ≥ 425, using
(26, 26+50, 49999)-Net in Base 64 — Upper bound on s
There is no (26, 76, 50000)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 186127 110310 079583 025885 696083 592384 123430 160207 242085 623728 327099 759092 032564 801396 118599 929341 435213 595233 513956 270115 530597 721586 132876 > 6476 [i]