Best Known (110−15, 110, s)-Nets in Base 4
(110−15, 110, 37465)-Net over F4 — Constructive and digital
Digital (95, 110, 37465)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 10, 15)-net over F4, using
- digital (85, 100, 37450)-net over F4, using
- net defined by OOA [i] based on linear OOA(4100, 37450, F4, 15, 15) (dual of [(37450, 15), 561650, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4100, 262151, F4, 15) (dual of [262151, 262051, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4100, 262153, F4, 15) (dual of [262153, 262053, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [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(491, 262144, F4, 14) (dual of [262144, 262053, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(40, 9, F4, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(4100, 262153, F4, 15) (dual of [262153, 262053, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4100, 262151, F4, 15) (dual of [262151, 262051, 16]-code), using
- net defined by OOA [i] based on linear OOA(4100, 37450, F4, 15, 15) (dual of [(37450, 15), 561650, 16]-NRT-code), using
(110−15, 110, 211012)-Net over F4 — Digital
Digital (95, 110, 211012)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4110, 211012, F4, 15) (dual of [211012, 210902, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4110, 262164, F4, 15) (dual of [262164, 262054, 16]-code), using
- (u, u+v)-construction [i] based on
- linear OA(410, 20, F4, 7) (dual of [20, 10, 8]-code), using
- extended quadratic residue code Qe(20,4) [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(410, 20, F4, 7) (dual of [20, 10, 8]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4110, 262164, F4, 15) (dual of [262164, 262054, 16]-code), using
(110−15, 110, large)-Net in Base 4 — Upper bound on s
There is no (95, 110, large)-net in base 4, because
- 13 times m-reduction [i] would yield (95, 97, large)-net in base 4, but