Best Known (77−47, 77, s)-Nets in Base 64
(77−47, 77, 513)-Net over F64 — Constructive and digital
Digital (30, 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
(77−47, 77, 139099)-Net in Base 64 — Upper bound on s
There is no (30, 77, 139100)-net in base 64, because
- 1 times m-reduction [i] would yield (30, 76, 139100)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 186070 822990 779287 151654 586815 013430 485819 187276 347999 217317 354436 284797 650963 117114 587101 249184 160211 651043 009036 745074 457261 906701 532506 > 6476 [i]