Best Known (33−19, 33, s)-Nets in Base 27
(33−19, 33, 102)-Net over F27 — Constructive and digital
Digital (14, 33, 102)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- digital (4, 23, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (1, 10, 38)-net over F27, using
(33−19, 33, 136)-Net over F27 — Digital
Digital (14, 33, 136)-net over F27, using
- t-expansion [i] based on digital (13, 33, 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
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
(33−19, 33, 160)-Net in Base 27 — Constructive
(14, 33, 160)-net in base 27, using
- 3 times m-reduction [i] based on (14, 36, 160)-net in base 27, using
- base change [i] based on digital (5, 27, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- base change [i] based on digital (5, 27, 160)-net over F81, using
(33−19, 33, 167)-Net in Base 27
(14, 33, 167)-net in base 27, using
- 3 times m-reduction [i] based on (14, 36, 167)-net in base 27, using
- base change [i] based on digital (5, 27, 167)-net over F81, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- base change [i] based on digital (5, 27, 167)-net over F81, using
(33−19, 33, 19587)-Net in Base 27 — Upper bound on s
There is no (14, 33, 19588)-net in base 27, because
- 1 times m-reduction [i] would yield (14, 32, 19588)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 6364 657781 546252 027781 443001 163725 783486 342761 > 2732 [i]