Best Known (156, 156+44, s)-Nets in Base 4
(156, 156+44, 1052)-Net over F4 — Constructive and digital
Digital (156, 200, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 50, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
(156, 156+44, 3887)-Net over F4 — Digital
Digital (156, 200, 3887)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4200, 3887, F4, 44) (dual of [3887, 3687, 45]-code), using
- discarding factors / shortening the dual code based on linear OA(4200, 4109, F4, 44) (dual of [4109, 3909, 45]-code), using
- construction X applied to Ce(44) ⊂ Ce(41) [i] based on
- linear OA(4199, 4096, F4, 45) (dual of [4096, 3897, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(4187, 4096, F4, 42) (dual of [4096, 3909, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [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(44) ⊂ Ce(41) [i] based on
- discarding factors / shortening the dual code based on linear OA(4200, 4109, F4, 44) (dual of [4109, 3909, 45]-code), using
(156, 156+44, 897420)-Net in Base 4 — Upper bound on s
There is no (156, 200, 897421)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2 582307 090973 379515 989496 599565 048720 904424 191647 730181 625089 620227 003893 805308 880154 384466 738844 403844 322699 457490 966496 > 4200 [i]