Best Known (5, 5+31, s)-Nets in Base 27
(5, 5+31, 68)-Net over F27 — Constructive and digital
Digital (5, 36, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
(5, 5+31, 72)-Net over F27 — Digital
Digital (5, 36, 72)-net over F27, using
- net from sequence [i] based on digital (5, 71)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 72, using
(5, 5+31, 532)-Net in Base 27 — Upper bound on s
There is no (5, 36, 533)-net in base 27, because
- 1 times m-reduction [i] would yield (5, 35, 533)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 126 084691 341046 428405 549003 977168 850204 634407 652035 > 2735 [i]