Best Known (34−19, 34, s)-Nets in Base 27
(34−19, 34, 112)-Net over F27 — Constructive and digital
Digital (15, 34, 112)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 11, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-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 (2, 11, 48)-net over F27, using
(34−19, 34, 157)-Net over F27 — Digital
Digital (15, 34, 157)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2734, 157, F27, 19) (dual of [157, 123, 20]-code), using
- 19 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 16 times 0) [i] based on linear OA(2732, 136, F27, 19) (dual of [136, 104, 20]-code), using
- extended algebraic-geometric code AGe(F,116P) [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
- 19 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 16 times 0) [i] based on linear OA(2732, 136, F27, 19) (dual of [136, 104, 20]-code), using
(34−19, 34, 160)-Net in Base 27 — Constructive
(15, 34, 160)-net in base 27, using
- 6 times m-reduction [i] based on (15, 40, 160)-net in base 27, using
- base change [i] based on digital (5, 30, 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, 30, 160)-net over F81, using
(34−19, 34, 190)-Net in Base 27
(15, 34, 190)-net in base 27, using
- 2 times m-reduction [i] based on (15, 36, 190)-net in base 27, using
- base change [i] based on digital (6, 27, 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, 27, 190)-net over F81, using
(34−19, 34, 28251)-Net in Base 27 — Upper bound on s
There is no (15, 34, 28252)-net in base 27, because
- 1 times m-reduction [i] would yield (15, 33, 28252)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 171807 095433 439946 946686 832522 596438 951962 081241 > 2733 [i]