Best Known (184−38, 184, s)-Nets in Base 4
(184−38, 184, 1060)-Net over F4 — Constructive and digital
Digital (146, 184, 1060)-net over F4, using
- trace code for nets [i] based on digital (8, 46, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
(184−38, 184, 4844)-Net over F4 — Digital
Digital (146, 184, 4844)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4184, 4844, F4, 38) (dual of [4844, 4660, 39]-code), using
- 727 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 4 times 0, 1, 7 times 0, 1, 12 times 0, 1, 19 times 0, 1, 31 times 0, 1, 47 times 0, 1, 68 times 0, 1, 95 times 0, 1, 121 times 0, 1, 145 times 0, 1, 164 times 0) [i] based on linear OA(4169, 4102, F4, 38) (dual of [4102, 3933, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(36) [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(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(40, 6, F4, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(37) ⊂ Ce(36) [i] based on
- 727 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 4 times 0, 1, 7 times 0, 1, 12 times 0, 1, 19 times 0, 1, 31 times 0, 1, 47 times 0, 1, 68 times 0, 1, 95 times 0, 1, 121 times 0, 1, 145 times 0, 1, 164 times 0) [i] based on linear OA(4169, 4102, F4, 38) (dual of [4102, 3933, 39]-code), using
(184−38, 184, 1788818)-Net in Base 4 — Upper bound on s
There is no (146, 184, 1788819)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 601 231230 529869 437903 293668 325926 732579 802794 641418 398860 225581 719886 545193 184087 026964 859497 833704 729863 770988 > 4184 [i]