Best Known (30−21, 30, s)-Nets in Base 27
(30−21, 30, 88)-Net over F27 — Constructive and digital
Digital (9, 30, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
(30−21, 30, 99)-Net over F27 — Digital
Digital (9, 30, 99)-net over F27, using
- net from sequence [i] based on digital (9, 98)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 99, using
(30−21, 30, 100)-Net in Base 27 — Constructive
(9, 30, 100)-net in base 27, using
- 2 times m-reduction [i] based on (9, 32, 100)-net in base 27, using
- base change [i] based on digital (1, 24, 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, 24, 100)-net over F81, using
(30−21, 30, 2460)-Net in Base 27 — Upper bound on s
There is no (9, 30, 2461)-net in base 27, because
- 1 times m-reduction [i] would yield (9, 29, 2461)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 323365 534276 332353 609579 795852 199279 007473 > 2729 [i]