Best Known (40−12, 40, s)-Nets in Base 3
(40−12, 40, 114)-Net over F3 — Constructive and digital
Digital (28, 40, 114)-net over F3, using
- 31 times duplication [i] based on digital (27, 39, 114)-net over F3, using
- trace code for nets [i] based on digital (1, 13, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- trace code for nets [i] based on digital (1, 13, 38)-net over F27, using
(40−12, 40, 156)-Net over F3 — Digital
Digital (28, 40, 156)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(340, 156, F3, 12) (dual of [156, 116, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(340, 242, F3, 12) (dual of [242, 202, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(340, 242, F3, 12) (dual of [242, 202, 13]-code), using
(40−12, 40, 2264)-Net in Base 3 — Upper bound on s
There is no (28, 40, 2265)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 12 177835 352375 642697 > 340 [i]