Best Known (31, 77, s)-Nets in Base 64
(31, 77, 513)-Net over F64 — Constructive and digital
Digital (31, 77, 513)-net over F64, using
- t-expansion [i] based on digital (28, 77, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(31, 77, 166671)-Net in Base 64 — Upper bound on s
There is no (31, 77, 166672)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 11 908585 266077 455140 813484 043595 954357 709099 190541 547839 009199 405794 202426 807545 824393 998646 144438 894615 835050 607413 146159 155566 047624 711408 > 6477 [i]