Best Known (9, 24, s)-Nets in Base 27
(9, 24, 88)-Net over F27 — Constructive and digital
Digital (9, 24, 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
(9, 24, 99)-Net over F27 — Digital
Digital (9, 24, 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
(9, 24, 116)-Net in Base 27 — Constructive
(9, 24, 116)-net in base 27, using
- 4 times m-reduction [i] based on (9, 28, 116)-net in base 27, using
- base change [i] based on digital (2, 21, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 21, 116)-net over F81, using
(9, 24, 136)-Net in Base 27
(9, 24, 136)-net in base 27, using
- base change [i] based on digital (3, 18, 136)-net over F81, using
- net from sequence [i] based on digital (3, 135)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 3 and N(F) ≥ 136, using
- net from sequence [i] based on digital (3, 135)-sequence over F81, using
(9, 24, 6558)-Net in Base 27 — Upper bound on s
There is no (9, 24, 6559)-net in base 27, because
- 1 times m-reduction [i] would yield (9, 23, 6559)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 835 143314 272357 240912 361162 312907 > 2723 [i]