Best Known (55−42, 55, s)-Nets in Base 27
(55−42, 55, 96)-Net over F27 — Constructive and digital
Digital (13, 55, 96)-net over F27, using
- t-expansion [i] based on digital (11, 55, 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
(55−42, 55, 136)-Net over F27 — Digital
Digital (13, 55, 136)-net over F27, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
(55−42, 55, 1861)-Net in Base 27 — Upper bound on s
There is no (13, 55, 1862)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 5 350370 625702 906892 337199 440224 245978 392857 547380 851060 195652 809567 197307 032917 > 2755 [i]