Best Known (176−38, 176, s)-Nets in Base 4
(176−38, 176, 1052)-Net over F4 — Constructive and digital
Digital (138, 176, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 44, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(176−38, 176, 3992)-Net over F4 — Digital
Digital (138, 176, 3992)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4176, 3992, F4, 38) (dual of [3992, 3816, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(4176, 4127, F4, 38) (dual of [4127, 3951, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(32) [i] based on
- linear OA(4169, 4096, F4, 38) (dual of [4096, 3927, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(4145, 4096, F4, 33) (dual of [4096, 3951, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(47, 31, F4, 4) (dual of [31, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(37) ⊂ Ce(32) [i] based on
- discarding factors / shortening the dual code based on linear OA(4176, 4127, F4, 38) (dual of [4127, 3951, 39]-code), using
(176−38, 176, 997847)-Net in Base 4 — Upper bound on s
There is no (138, 176, 997848)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 9174 015019 798001 301148 471140 660968 055589 358992 801476 602404 930885 072398 044690 195230 294383 455779 475605 691581 > 4176 [i]