Best Known (19, 19+9, s)-Nets in Base 3
(19, 19+9, 84)-Net over F3 — Constructive and digital
Digital (19, 28, 84)-net over F3, using
- 31 times duplication [i] based on digital (18, 27, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 9, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- trace code for nets [i] based on digital (0, 9, 28)-net over F27, using
(19, 19+9, 112)-Net over F3 — Digital
Digital (19, 28, 112)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(328, 112, F3, 9) (dual of [112, 84, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(328, 125, F3, 9) (dual of [125, 97, 10]-code), using
- a “BZ†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(328, 125, F3, 9) (dual of [125, 97, 10]-code), using
(19, 19+9, 1835)-Net in Base 3 — Upper bound on s
There is no (19, 28, 1836)-net in base 3, because
- 1 times m-reduction [i] would yield (19, 27, 1836)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 7 633176 071041 > 327 [i]