Best Known (30, 42, s)-Nets in Base 3
(30, 42, 144)-Net over F3 — Constructive and digital
Digital (30, 42, 144)-net over F3, using
- trace code for nets [i] based on digital (2, 14, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
(30, 42, 197)-Net over F3 — Digital
Digital (30, 42, 197)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(342, 197, F3, 12) (dual of [197, 155, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(342, 254, F3, 12) (dual of [254, 212, 13]-code), using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(341, 243, F3, 13) (dual of [243, 202, 14]-code), using an extension Ce(12) of 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]
- linear OA(331, 243, F3, 10) (dual of [243, 212, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(342, 254, F3, 12) (dual of [254, 212, 13]-code), using
(30, 42, 3268)-Net in Base 3 — Upper bound on s
There is no (30, 42, 3269)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 109 575726 801858 860481 > 342 [i]