Best Known (76, 86, s)-Nets in Base 4
(76, 86, 1677720)-Net over F4 — Constructive and digital
Digital (76, 86, 1677720)-net over F4, using
- 41 times duplication [i] based on digital (75, 85, 1677720)-net over F4, using
- net defined by OOA [i] based on linear OOA(485, 1677720, F4, 10, 10) (dual of [(1677720, 10), 16777115, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(485, 8388600, F4, 10) (dual of [8388600, 8388515, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(485, large, F4, 10) (dual of [large, large−85, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(485, large, F4, 10) (dual of [large, large−85, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(485, 8388600, F4, 10) (dual of [8388600, 8388515, 11]-code), using
- net defined by OOA [i] based on linear OOA(485, 1677720, F4, 10, 10) (dual of [(1677720, 10), 16777115, 11]-NRT-code), using
(76, 86, 4194301)-Net over F4 — Digital
Digital (76, 86, 4194301)-net over F4, using
- 41 times duplication [i] based on digital (75, 85, 4194301)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(485, 4194301, F4, 2, 10) (dual of [(4194301, 2), 8388517, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(485, 8388602, F4, 10) (dual of [8388602, 8388517, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(485, large, F4, 10) (dual of [large, large−85, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(485, large, F4, 10) (dual of [large, large−85, 11]-code), using
- OOA 2-folding [i] based on linear OA(485, 8388602, F4, 10) (dual of [8388602, 8388517, 11]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(485, 4194301, F4, 2, 10) (dual of [(4194301, 2), 8388517, 11]-NRT-code), using
(76, 86, large)-Net in Base 4 — Upper bound on s
There is no (76, 86, large)-net in base 4, because
- 8 times m-reduction [i] would yield (76, 78, large)-net in base 4, but