Best Known (78−50, 78, s)-Nets in Base 64
(78−50, 78, 513)-Net over F64 — Constructive and digital
Digital (28, 78, 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
(78−50, 78, 69741)-Net in Base 64 — Upper bound on s
There is no (28, 78, 69742)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 762 355750 331213 325823 358497 133838 469414 128319 204278 837858 284168 118175 101654 930651 286209 527115 746290 387991 858581 983597 705357 209882 105514 154006 > 6478 [i]