Best Known (107, 130, s)-Nets in Base 4
(107, 130, 1493)-Net over F4 — Constructive and digital
Digital (107, 130, 1493)-net over F4, using
- net defined by OOA [i] based on linear OOA(4130, 1493, F4, 23, 23) (dual of [(1493, 23), 34209, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4130, 16424, F4, 23) (dual of [16424, 16294, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4130, 16429, F4, 23) (dual of [16429, 16299, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(485, 16384, F4, 17) (dual of [16384, 16299, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(410, 45, F4, 5) (dual of [45, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(4130, 16429, F4, 23) (dual of [16429, 16299, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4130, 16424, F4, 23) (dual of [16424, 16294, 24]-code), using
(107, 130, 14429)-Net over F4 — Digital
Digital (107, 130, 14429)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4130, 14429, F4, 23) (dual of [14429, 14299, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4130, 16429, F4, 23) (dual of [16429, 16299, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(485, 16384, F4, 17) (dual of [16384, 16299, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(410, 45, F4, 5) (dual of [45, 35, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(4130, 16429, F4, 23) (dual of [16429, 16299, 24]-code), using
(107, 130, large)-Net in Base 4 — Upper bound on s
There is no (107, 130, large)-net in base 4, because
- 21 times m-reduction [i] would yield (107, 109, large)-net in base 4, but