Best Known (143, 183, s)-Nets in Base 4
(143, 183, 1048)-Net over F4 — Constructive and digital
Digital (143, 183, 1048)-net over F4, using
- 1 times m-reduction [i] based on digital (143, 184, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 46, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
- trace code for nets [i] based on digital (5, 46, 262)-net over F256, using
(143, 183, 3800)-Net over F4 — Digital
Digital (143, 183, 3800)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4183, 3800, F4, 40) (dual of [3800, 3617, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(4183, 4111, F4, 40) (dual of [4111, 3928, 41]-code), using
- construction XX applied to Ce(40) ⊂ Ce(37) ⊂ 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(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(41, 14, F4, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, 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(40) ⊂ Ce(37) ⊂ Ce(36) [i] based on
- discarding factors / shortening the dual code based on linear OA(4183, 4111, F4, 40) (dual of [4111, 3928, 41]-code), using
(143, 183, 893359)-Net in Base 4 — Upper bound on s
There is no (143, 183, 893360)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 150 309946 968734 052304 301341 434451 004006 088018 849411 155510 545648 763299 777451 341812 830930 451445 035214 064381 331514 > 4183 [i]