Best Known (116−22, 116, s)-Nets in Base 4
(116−22, 116, 1491)-Net over F4 — Constructive and digital
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
(116−22, 116, 8200)-Net over F4 — Digital
Digital (94, 116, 8200)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4116, 8200, F4, 2, 22) (dual of [(8200, 2), 16284, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4116, 16400, F4, 22) (dual of [16400, 16284, 23]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(4116, 16401, F4, 22) (dual of [16401, 16285, 23]-code), using
- OOA 2-folding [i] based on linear OA(4116, 16400, F4, 22) (dual of [16400, 16284, 23]-code), using
(116−22, 116, 3655006)-Net in Base 4 — Upper bound on s
There is no (94, 116, 3655007)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 6901 758440 673919 316712 809616 762752 576449 381921 739769 031503 140485 976320 > 4116 [i]