Best Known (95, 107, s)-Nets in Base 4
(95, 107, 699062)-Net over F4 — Constructive and digital
Digital (95, 107, 699062)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (2, 8, 12)-net over F4, using
- digital (87, 99, 699050)-net over F4, using
- net defined by OOA [i] based on linear OOA(499, 699050, F4, 12, 12) (dual of [(699050, 12), 8388501, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(499, 4194300, F4, 12) (dual of [4194300, 4194201, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(499, 4194303, F4, 12) (dual of [4194303, 4194204, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(499, 4194303, F4, 12) (dual of [4194303, 4194204, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(499, 4194300, F4, 12) (dual of [4194300, 4194201, 13]-code), using
- net defined by OOA [i] based on linear OOA(499, 699050, F4, 12, 12) (dual of [(699050, 12), 8388501, 13]-NRT-code), using
(95, 107, 3636554)-Net over F4 — Digital
Digital (95, 107, 3636554)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4107, 3636554, F4, 12) (dual of [3636554, 3636447, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4107, 4194347, F4, 12) (dual of [4194347, 4194240, 13]-code), using
- construction X applied to Ce(12) ⊂ Ce(6) [i] based on
- linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(456, 4194304, F4, 7) (dual of [4194304, 4194248, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, 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(4107, 4194347, F4, 12) (dual of [4194347, 4194240, 13]-code), using
(95, 107, large)-Net in Base 4 — Upper bound on s
There is no (95, 107, large)-net in base 4, because
- 10 times m-reduction [i] would yield (95, 97, large)-net in base 4, but