Best Known (33−27, 33, s)-Nets in Base 81
(33−27, 33, 160)-Net over F81 — Constructive and digital
Digital (6, 33, 160)-net over F81, using
- t-expansion [i] based on digital (5, 33, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
(33−27, 33, 190)-Net over F81 — Digital
Digital (6, 33, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
(33−27, 33, 3526)-Net in Base 81 — Upper bound on s
There is no (6, 33, 3527)-net in base 81, because
- 1 times m-reduction [i] would yield (6, 32, 3527)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 11 803555 940137 910567 213225 272740 768891 673340 323074 976992 493681 > 8132 [i]