Best Known (96, 96+22, s)-Nets in Base 4
(96, 96+22, 1491)-Net over F4 — Constructive and digital
Digital (96, 118, 1491)-net over F4, using
- 42 times duplication [i] based on digital (94, 116, 1491)-net over F4, using
- net defined by OOA [i] based on linear OOA(4116, 1491, F4, 22, 22) (dual of [(1491, 22), 32686, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(4116, 16401, F4, 22) (dual of [16401, 16285, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(499, 16384, F4, 19) (dual of [16384, 16285, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(43, 17, F4, 2) (dual of [17, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
- OA 11-folding and stacking [i] based on linear OA(4116, 16401, F4, 22) (dual of [16401, 16285, 23]-code), using
- net defined by OOA [i] based on linear OOA(4116, 1491, F4, 22, 22) (dual of [(1491, 22), 32686, 23]-NRT-code), using
(96, 96+22, 9194)-Net over F4 — Digital
Digital (96, 118, 9194)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4118, 9194, F4, 22) (dual of [9194, 9076, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4118, 16410, F4, 22) (dual of [16410, 16292, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(492, 16384, F4, 18) (dual of [16384, 16292, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(45, 26, F4, 3) (dual of [26, 21, 4]-code or 26-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
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(4118, 16410, F4, 22) (dual of [16410, 16292, 23]-code), using
(96, 96+22, 4702770)-Net in Base 4 — Upper bound on s
There is no (96, 118, 4702771)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 110427 955973 304710 237982 692740 549019 816885 385216 493715 880971 931678 085384 > 4118 [i]