Best Known (81−53, 81, s)-Nets in Base 64
(81−53, 81, 513)-Net over F64 — Constructive and digital
Digital (28, 81, 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
(81−53, 81, 60441)-Net in Base 64 — Upper bound on s
There is no (28, 81, 60442)-net in base 64, because
- 1 times m-reduction [i] would yield (28, 80, 60442)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 3 122171 197727 377963 935919 780797 609914 885332 064112 195627 866074 092194 241338 840573 646779 213503 206169 179010 762992 634773 350405 848804 115442 387681 957760 > 6480 [i]