Best Known (20, 20+9, s)-Nets in Base 3
(20, 20+9, 84)-Net over F3 — Constructive and digital
Digital (20, 29, 84)-net over F3, using
- 1 times m-reduction [i] based on digital (20, 30, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 10, 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, 10, 28)-net over F27, using
(20, 20+9, 131)-Net over F3 — Digital
Digital (20, 29, 131)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(329, 131, F3, 9) (dual of [131, 102, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(329, 140, F3, 9) (dual of [140, 111, 10]-code), using
- a “BZ†code from Brouwer’s database [i]
- discarding factors / shortening the dual code based on linear OA(329, 140, F3, 9) (dual of [140, 111, 10]-code), using
(20, 20+9, 2416)-Net in Base 3 — Upper bound on s
There is no (20, 29, 2417)-net in base 3, because
- 1 times m-reduction [i] would yield (20, 28, 2417)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 22 883769 782737 > 328 [i]