Best Known (151, 193, s)-Nets in Base 4
(151, 193, 1052)-Net over F4 — Constructive and digital
Digital (151, 193, 1052)-net over F4, using
- 41 times duplication [i] based on digital (150, 192, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 48, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
- trace code for nets [i] based on digital (6, 48, 263)-net over F256, using
(151, 193, 4047)-Net over F4 — Digital
Digital (151, 193, 4047)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4193, 4047, F4, 42) (dual of [4047, 3854, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(4193, 4121, F4, 42) (dual of [4121, 3928, 43]-code), using
- construction XX applied to Ce(41) ⊂ Ce(37) ⊂ Ce(36) [i] based on
- 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(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(45, 24, F4, 3) (dual of [24, 19, 4]-code or 24-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(41) ⊂ Ce(37) ⊂ Ce(36) [i] based on
- discarding factors / shortening the dual code based on linear OA(4193, 4121, F4, 42) (dual of [4121, 3928, 43]-code), using
(151, 193, 987601)-Net in Base 4 — Upper bound on s
There is no (151, 193, 987602)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 157 608850 080262 052850 278814 151832 521805 599942 632724 807282 263588 232761 207534 787476 266201 602982 576183 992427 414302 010032 > 4193 [i]