Best Known (60, 60+14, s)-Nets in Base 4
(60, 60+14, 2343)-Net over F4 — Constructive and digital
Digital (60, 74, 2343)-net over F4, using
- net defined by OOA [i] based on linear OOA(474, 2343, F4, 14, 14) (dual of [(2343, 14), 32728, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(474, 16401, F4, 14) (dual of [16401, 16327, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(471, 16384, F4, 14) (dual of [16384, 16313, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(457, 16384, F4, 11) (dual of [16384, 16327, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(13) ⊂ Ce(10) [i] based on
- OA 7-folding and stacking [i] based on linear OA(474, 16401, F4, 14) (dual of [16401, 16327, 15]-code), using
(60, 60+14, 8200)-Net over F4 — Digital
Digital (60, 74, 8200)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(474, 8200, F4, 2, 14) (dual of [(8200, 2), 16326, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(474, 16400, F4, 14) (dual of [16400, 16326, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(474, 16401, F4, 14) (dual of [16401, 16327, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(471, 16384, F4, 14) (dual of [16384, 16313, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(457, 16384, F4, 11) (dual of [16384, 16327, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(13) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(474, 16401, F4, 14) (dual of [16401, 16327, 15]-code), using
- OOA 2-folding [i] based on linear OA(474, 16400, F4, 14) (dual of [16400, 16326, 15]-code), using
(60, 60+14, 2608739)-Net in Base 4 — Upper bound on s
There is no (60, 74, 2608740)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 356 812485 644571 575209 769595 444330 995002 537480 > 474 [i]