Best Known (28−16, 28, s)-Nets in Base 27
(28−16, 28, 96)-Net over F27 — Constructive and digital
Digital (12, 28, 96)-net over F27, using
- t-expansion [i] based on digital (11, 28, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(28−16, 28, 125)-Net over F27 — Digital
Digital (12, 28, 125)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2728, 125, F27, 16) (dual of [125, 97, 17]-code), using
- 23 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 16 times 0) [i] based on linear OA(2725, 99, F27, 16) (dual of [99, 74, 17]-code), using
- extended algebraic-geometric code AGe(F,82P) [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 99, using
- 23 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 16 times 0) [i] based on linear OA(2725, 99, F27, 16) (dual of [99, 74, 17]-code), using
(28−16, 28, 160)-Net in Base 27 — Constructive
(12, 28, 160)-net in base 27, using
- base change [i] based on digital (5, 21, 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
(28−16, 28, 167)-Net in Base 27
(12, 28, 167)-net in base 27, using
- base change [i] based on digital (5, 21, 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
(28−16, 28, 14803)-Net in Base 27 — Upper bound on s
There is no (12, 28, 14804)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 11972 706219 265745 649288 107726 002667 096001 > 2728 [i]