Best Known (4, 4+68, s)-Nets in Base 27
(4, 4+68, 64)-Net over F27 — Constructive and digital
Digital (4, 72, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
(4, 4+68, 426)-Net in Base 27 — Upper bound on s
There is no (4, 72, 427)-net in base 27, because
- 36 times m-reduction [i] would yield (4, 36, 427)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 3436 062497 260181 972124 596613 580627 151009 391248 440929 > 2736 [i]