Best Known (14, 32, s)-Nets in Base 27
(14, 32, 102)-Net over F27 — Constructive and digital
Digital (14, 32, 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, 22, 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
(14, 32, 147)-Net over F27 — Digital
Digital (14, 32, 147)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2732, 147, F27, 18) (dual of [147, 115, 19]-code), using
- 10 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0) [i] based on linear OA(2731, 136, F27, 18) (dual of [136, 105, 19]-code), using
- extended algebraic-geometric code AGe(F,117P) [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
- 10 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0) [i] based on linear OA(2731, 136, F27, 18) (dual of [136, 105, 19]-code), using
(14, 32, 160)-Net in Base 27 — Constructive
(14, 32, 160)-net in base 27, using
- 4 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
(14, 32, 190)-Net in Base 27
(14, 32, 190)-net in base 27, using
- base change [i] based on digital (6, 24, 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
(14, 32, 19587)-Net in Base 27 — Upper bound on s
There is no (14, 32, 19588)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 6364 657781 546252 027781 443001 163725 783486 342761 > 2732 [i]