Best Known (32, 32+45, s)-Nets in Base 64
(32, 32+45, 513)-Net over F64 — Constructive and digital
Digital (32, 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
(32, 32+45, 249473)-Net in Base 64 — Upper bound on s
There is no (32, 77, 249474)-net in base 64, because
- 1 times m-reduction [i] would yield (32, 76, 249474)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 186079 007622 215331 265038 326024 127704 875539 724254 059147 859391 428415 549951 057703 339309 655796 181201 319812 183295 116406 433868 173679 316291 355840 > 6476 [i]