Best Known (54−42, 54, s)-Nets in Base 27
(54−42, 54, 96)-Net over F27 — Constructive and digital
Digital (12, 54, 96)-net over F27, using
- t-expansion [i] based on digital (11, 54, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(54−42, 54, 109)-Net over F27 — Digital
Digital (12, 54, 109)-net over F27, using
- net from sequence [i] based on digital (12, 108)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 12 and N(F) ≥ 109, using
(54−42, 54, 1589)-Net in Base 27 — Upper bound on s
There is no (12, 54, 1590)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 198209 211927 978420 881415 028956 706270 375419 993763 479138 627952 598016 703971 753269 > 2754 [i]