Best Known (86, 98, s)-Nets in Base 4
(86, 98, 174774)-Net over F4 — Constructive and digital
Digital (86, 98, 174774)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (2, 8, 12)-net over F4, using
- digital (78, 90, 174762)-net over F4, using
- net defined by OOA [i] based on linear OOA(490, 174762, F4, 12, 12) (dual of [(174762, 12), 2097054, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(490, 1048572, F4, 12) (dual of [1048572, 1048482, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(490, 1048575, F4, 12) (dual of [1048575, 1048485, 13]-code), using
- 1 times truncation [i] based on linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 1 times truncation [i] based on linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(490, 1048575, F4, 12) (dual of [1048575, 1048485, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(490, 1048572, F4, 12) (dual of [1048572, 1048482, 13]-code), using
- net defined by OOA [i] based on linear OOA(490, 174762, F4, 12, 12) (dual of [(174762, 12), 2097054, 13]-NRT-code), using
(86, 98, 1044321)-Net over F4 — Digital
Digital (86, 98, 1044321)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(498, 1044321, F4, 12) (dual of [1044321, 1044223, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(498, 1048619, F4, 12) (dual of [1048619, 1048521, 13]-code), using
- construction X applied to Ce(12) ⊂ Ce(6) [i] based on
- linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(451, 1048576, F4, 7) (dual of [1048576, 1048525, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(12) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(498, 1048619, F4, 12) (dual of [1048619, 1048521, 13]-code), using
(86, 98, large)-Net in Base 4 — Upper bound on s
There is no (86, 98, large)-net in base 4, because
- 10 times m-reduction [i] would yield (86, 88, large)-net in base 4, but