Best Known (31, 31+49, s)-Nets in Base 64
(31, 31+49, 513)-Net over F64 — Constructive and digital
Digital (31, 80, 513)-net over F64, using
- t-expansion [i] based on digital (28, 80, 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, 31+49, 137191)-Net in Base 64 — Upper bound on s
There is no (31, 80, 137192)-net in base 64, because
- 1 times m-reduction [i] would yield (31, 79, 137192)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 48782 157630 479496 702701 896444 848519 354954 066390 816729 033042 859413 196361 214277 946035 002958 331125 265267 411392 089614 443317 279406 767718 437992 721436 > 6479 [i]