Best Known (144, 184, s)-Nets in Base 4
(144, 184, 1052)-Net over F4 — Constructive and digital
Digital (144, 184, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 46, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(144, 184, 3943)-Net over F4 — Digital
Digital (144, 184, 3943)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4184, 3943, F4, 40) (dual of [3943, 3759, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(4184, 4117, F4, 40) (dual of [4117, 3933, 41]-code), using
- construction X applied to Ce(40) ⊂ Ce(36) [i] based on
- linear OA(4181, 4096, F4, 41) (dual of [4096, 3915, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(4163, 4096, F4, 37) (dual of [4096, 3933, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(40) ⊂ Ce(36) [i] based on
- discarding factors / shortening the dual code based on linear OA(4184, 4117, F4, 40) (dual of [4117, 3933, 41]-code), using
(144, 184, 957479)-Net in Base 4 — Upper bound on s
There is no (144, 184, 957480)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 601 230986 719185 519895 239923 114948 849649 754752 406695 791941 264230 006456 218546 461521 488145 168889 486305 929241 165466 > 4184 [i]