Best Known (18, 26, s)-Nets in Base 3
(18, 26, 84)-Net over F3 — Constructive and digital
Digital (18, 26, 84)-net over F3, using
- 1 times m-reduction [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
(18, 26, 141)-Net over F3 — Digital
Digital (18, 26, 141)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(326, 141, F3, 8) (dual of [141, 115, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(326, 242, F3, 8) (dual of [242, 216, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(326, 242, F3, 8) (dual of [242, 216, 9]-code), using
(18, 26, 1393)-Net in Base 3 — Upper bound on s
There is no (18, 26, 1394)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 542795 606313 > 326 [i]