Best Known (5, 5+9, s)-Nets in Base 27
(5, 5+9, 68)-Net over F27 — Constructive and digital
Digital (5, 14, 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+9, 72)-Net over F27 — Digital
Digital (5, 14, 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+9, 100)-Net in Base 27 — Constructive
(5, 14, 100)-net in base 27, using
- 2 times m-reduction [i] based on (5, 16, 100)-net in base 27, using
- base change [i] based on digital (1, 12, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- base change [i] based on digital (1, 12, 100)-net over F81, using
(5, 5+9, 3817)-Net in Base 27 — Upper bound on s
There is no (5, 14, 3818)-net in base 27, because
- 1 times m-reduction [i] would yield (5, 13, 3818)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 4 053013 733105 024169 > 2713 [i]