Best Known (142, 182, s)-Nets in Base 4
(142, 182, 1048)-Net over F4 — Constructive and digital
Digital (142, 182, 1048)-net over F4, using
- 42 times duplication [i] based on digital (140, 180, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 45, 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, 45, 262)-net over F256, using
(142, 182, 3663)-Net over F4 — Digital
Digital (142, 182, 3663)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4182, 3663, F4, 40) (dual of [3663, 3481, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(4182, 4109, F4, 40) (dual of [4109, 3927, 41]-code), using
- construction X applied to Ce(40) ⊂ Ce(37) [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(41, 13, F4, 1) (dual of [13, 12, 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
- construction X applied to Ce(40) ⊂ Ce(37) [i] based on
- discarding factors / shortening the dual code based on linear OA(4182, 4109, F4, 40) (dual of [4109, 3927, 41]-code), using
(142, 182, 833532)-Net in Base 4 — Upper bound on s
There is no (142, 182, 833533)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 37 577242 671268 151134 846350 994119 801429 157693 708867 322078 760790 798099 265938 804155 276917 396129 985721 910571 225499 > 4182 [i]