Best Known (87, 106, s)-Nets in Base 4
(87, 106, 1824)-Net over F4 — Constructive and digital
Digital (87, 106, 1824)-net over F4, using
- net defined by OOA [i] based on linear OOA(4106, 1824, F4, 19, 19) (dual of [(1824, 19), 34550, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4106, 16417, F4, 19) (dual of [16417, 16311, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4106, 16419, F4, 19) (dual of [16419, 16313, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- 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(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(47, 35, F4, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(4106, 16419, F4, 19) (dual of [16419, 16313, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4106, 16417, F4, 19) (dual of [16417, 16311, 20]-code), using
(87, 106, 12502)-Net over F4 — Digital
Digital (87, 106, 12502)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4106, 12502, F4, 19) (dual of [12502, 12396, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4106, 16419, F4, 19) (dual of [16419, 16313, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- 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(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(47, 35, F4, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(4106, 16419, F4, 19) (dual of [16419, 16313, 20]-code), using
(87, 106, large)-Net in Base 4 — Upper bound on s
There is no (87, 106, large)-net in base 4, because
- 17 times m-reduction [i] would yield (87, 89, large)-net in base 4, but