Best Known (64, 76, s)-Nets in Base 4
(64, 76, 10926)-Net over F4 — Constructive and digital
Digital (64, 76, 10926)-net over F4, using
- net defined by OOA [i] based on linear OOA(476, 10926, F4, 12, 12) (dual of [(10926, 12), 131036, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(476, 65556, F4, 12) (dual of [65556, 65480, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(476, 65557, F4, 12) (dual of [65557, 65481, 13]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(449, 65536, F4, 9) (dual of [65536, 65487, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(476, 65557, F4, 12) (dual of [65557, 65481, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(476, 65556, F4, 12) (dual of [65556, 65480, 13]-code), using
(64, 76, 49458)-Net over F4 — Digital
Digital (64, 76, 49458)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(476, 49458, F4, 12) (dual of [49458, 49382, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(476, 65557, F4, 12) (dual of [65557, 65481, 13]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(449, 65536, F4, 9) (dual of [65536, 65487, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(476, 65557, F4, 12) (dual of [65557, 65481, 13]-code), using
(64, 76, large)-Net in Base 4 — Upper bound on s
There is no (64, 76, large)-net in base 4, because
- 10 times m-reduction [i] would yield (64, 66, large)-net in base 4, but