Best Known (147, 147+40, s)-Nets in Base 3
(147, 147+40, 640)-Net over F3 — Constructive and digital
Digital (147, 187, 640)-net over F3, using
- t-expansion [i] based on digital (146, 187, 640)-net over F3, using
- 1 times m-reduction [i] based on digital (146, 188, 640)-net over F3, using
- trace code for nets [i] based on digital (5, 47, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- trace code for nets [i] based on digital (5, 47, 160)-net over F81, using
- 1 times m-reduction [i] based on digital (146, 188, 640)-net over F3, using
(147, 147+40, 1591)-Net over F3 — Digital
Digital (147, 187, 1591)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3187, 1591, F3, 40) (dual of [1591, 1404, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(3187, 2205, F3, 40) (dual of [2205, 2018, 41]-code), using
- construction X applied to Ce(39) ⊂ Ce(36) [i] based on
- linear OA(3183, 2187, F3, 40) (dual of [2187, 2004, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3169, 2187, F3, 37) (dual of [2187, 2018, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(34, 18, F3, 2) (dual of [18, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(39) ⊂ Ce(36) [i] based on
- discarding factors / shortening the dual code based on linear OA(3187, 2205, F3, 40) (dual of [2205, 2018, 41]-code), using
(147, 147+40, 120029)-Net in Base 3 — Upper bound on s
There is no (147, 187, 120030)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 166602 806169 839357 477171 897413 861191 592401 086788 193517 448134 504048 666289 073916 552668 690601 > 3187 [i]