Best Known (17, 17+25, s)-Nets in Base 27
(17, 17+25, 102)-Net over F27 — Constructive and digital
Digital (17, 42, 102)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 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, 29, 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, 13, 38)-net over F27, using
(17, 17+25, 144)-Net over F27 — Digital
Digital (17, 42, 144)-net over F27, using
- t-expansion [i] based on digital (16, 42, 144)-net over F27, using
- net from sequence [i] based on digital (16, 143)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 16 and N(F) ≥ 144, using
- net from sequence [i] based on digital (16, 143)-sequence over F27, using
(17, 17+25, 160)-Net in Base 27 — Constructive
(17, 42, 160)-net in base 27, using
- 6 times m-reduction [i] based on (17, 48, 160)-net in base 27, using
- base change [i] based on digital (5, 36, 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, 36, 160)-net over F81, using
(17, 17+25, 190)-Net in Base 27
(17, 42, 190)-net in base 27, using
- 2 times m-reduction [i] based on (17, 44, 190)-net in base 27, using
- base change [i] based on digital (6, 33, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- base change [i] based on digital (6, 33, 190)-net over F81, using
(17, 17+25, 15802)-Net in Base 27 — Upper bound on s
There is no (17, 42, 15803)-net in base 27, because
- 1 times m-reduction [i] would yield (17, 41, 15803)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 48549 319480 440982 673768 923074 644028 690539 209904 156981 197737 > 2741 [i]