Best Known (92, 92+15, s)-Nets in Base 4
(92, 92+15, 37455)-Net over F4 — Constructive and digital
Digital (92, 107, 37455)-net over F4, using
- net defined by OOA [i] based on linear OOA(4107, 37455, F4, 15, 15) (dual of [(37455, 15), 561718, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4107, 262186, F4, 15) (dual of [262186, 262079, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4107, 262187, F4, 15) (dual of [262187, 262080, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- linear OA(4100, 262144, F4, 15) (dual of [262144, 262044, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(464, 262144, F4, 10) (dual of [262144, 262080, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(14) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(4107, 262187, F4, 15) (dual of [262187, 262080, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4107, 262186, F4, 15) (dual of [262186, 262079, 16]-code), using
(92, 92+15, 153236)-Net over F4 — Digital
Digital (92, 107, 153236)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4107, 153236, F4, 15) (dual of [153236, 153129, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4107, 262152, F4, 15) (dual of [262152, 262045, 16]-code), using
- (u, u+v)-construction [i] based on
- linear OA(47, 8, F4, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,4)), using
- dual of repetition code with length 8 [i]
- linear OA(4100, 262144, F4, 15) (dual of [262144, 262044, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(47, 8, F4, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,4)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4107, 262152, F4, 15) (dual of [262152, 262045, 16]-code), using
(92, 92+15, large)-Net in Base 4 — Upper bound on s
There is no (92, 107, large)-net in base 4, because
- 13 times m-reduction [i] would yield (92, 94, large)-net in base 4, but