Best Known (7, 7+17, s)-Nets in Base 27
(7, 7+17, 82)-Net over F27 — Constructive and digital
Digital (7, 24, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
(7, 7+17, 100)-Net in Base 27 — Constructive
(7, 24, 100)-net in base 27, using
- base change [i] based on digital (1, 18, 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
(7, 7+17, 1883)-Net in Base 27 — Upper bound on s
There is no (7, 24, 1884)-net in base 27, because
- 1 times m-reduction [i] would yield (7, 23, 1884)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 835 458002 524237 323384 396992 136129 > 2723 [i]