Best Known (22, 22+27, s)-Nets in Base 3
(22, 22+27, 32)-Net over F3 — Constructive and digital
Digital (22, 49, 32)-net over F3, using
- t-expansion [i] based on digital (21, 49, 32)-net over F3, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 21 and N(F) ≥ 32, using
- net from sequence [i] based on digital (21, 31)-sequence over F3, using
(22, 22+27, 151)-Net in Base 3 — Upper bound on s
There is no (22, 49, 152)-net in base 3, because
- 1 times m-reduction [i] would yield (22, 48, 152)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 82426 277495 539013 399089 > 348 [i]