Best Known (56−47, 56, s)-Nets in Base 27
(56−47, 56, 88)-Net over F27 — Constructive and digital
Digital (9, 56, 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
(56−47, 56, 99)-Net over F27 — Digital
Digital (9, 56, 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
(56−47, 56, 948)-Net in Base 27 — Upper bound on s
There is no (9, 56, 949)-net in base 27, because
- 1 times m-reduction [i] would yield (9, 55, 949)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 5 407351 414160 039344 908051 940591 041737 413022 102552 555248 149262 053899 785854 149283 > 2755 [i]