Best Known (74−65, 74, s)-Nets in Base 27
(74−65, 74, 88)-Net over F27 — Constructive and digital
Digital (9, 74, 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
(74−65, 74, 99)-Net over F27 — Digital
Digital (9, 74, 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
(74−65, 74, 889)-Net in Base 27 — Upper bound on s
There is no (9, 74, 890)-net in base 27, because
- 1 times m-reduction [i] would yield (9, 73, 890)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 314 218033 254139 482245 983224 862441 658065 071185 984094 706978 499991 576588 022080 151222 707613 217320 595569 931073 > 2773 [i]