Best Known (146, 180, s)-Nets in Base 4
(146, 180, 1126)-Net over F4 — Constructive and digital
Digital (146, 180, 1126)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (27, 44, 98)-net over F4, using
- trace code for nets [i] based on digital (5, 22, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- trace code for nets [i] based on digital (5, 22, 49)-net over F16, using
- digital (102, 136, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 34, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 34, 257)-net over F256, using
- digital (27, 44, 98)-net over F4, using
(146, 180, 9918)-Net over F4 — Digital
Digital (146, 180, 9918)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4180, 9918, F4, 34) (dual of [9918, 9738, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(4180, 16403, F4, 34) (dual of [16403, 16223, 35]-code), using
- construction XX applied to Ce(33) ⊂ Ce(30) ⊂ Ce(29) [i] based on
- linear OA(4176, 16384, F4, 34) (dual of [16384, 16208, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(4162, 16384, F4, 31) (dual of [16384, 16222, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4155, 16384, F4, 30) (dual of [16384, 16229, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(43, 18, F4, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(33) ⊂ Ce(30) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(4180, 16403, F4, 34) (dual of [16403, 16223, 35]-code), using
(146, 180, 5669904)-Net in Base 4 — Upper bound on s
There is no (146, 180, 5669905)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2 348545 129218 353319 089683 367398 049939 199593 180342 256760 792465 423785 890363 898345 920309 102837 495218 521520 833604 > 4180 [i]