Best Known (5, 5+70, s)-Nets in Base 27
(5, 5+70, 68)-Net over F27 — Constructive and digital
Digital (5, 75, 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+70, 72)-Net over F27 — Digital
Digital (5, 75, 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+70, 519)-Net in Base 27 — Upper bound on s
There is no (5, 75, 520)-net in base 27, because
- 32 times m-reduction [i] would yield (5, 43, 520)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 35 959038 036446 135949 235694 992561 072019 501619 565612 743987 024993 > 2743 [i]