Best Known (119−13, 119, s)-Nets in Base 4
(119−13, 119, 1398126)-Net over F4 — Constructive and digital
Digital (106, 119, 1398126)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (4, 10, 26)-net over F4, using
- digital (96, 109, 1398100)-net over F4, using
- net defined by OOA [i] based on linear OOA(4109, 1398100, F4, 13, 13) (dual of [(1398100, 13), 18175191, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(4109, 8388601, F4, 13) (dual of [8388601, 8388492, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding factors / shortening the dual code based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(4109, 8388601, F4, 13) (dual of [8388601, 8388492, 14]-code), using
- net defined by OOA [i] based on linear OOA(4109, 1398100, F4, 13, 13) (dual of [(1398100, 13), 18175191, 14]-NRT-code), using
(119−13, 119, 4702771)-Net over F4 — Digital
Digital (106, 119, 4702771)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4119, 4702771, F4, 13) (dual of [4702771, 4702652, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4119, large, F4, 13) (dual of [large, large−119, 14]-code), using
- 10 times code embedding in larger space [i] based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- 10 times code embedding in larger space [i] based on linear OA(4109, large, F4, 13) (dual of [large, large−109, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(4119, large, F4, 13) (dual of [large, large−119, 14]-code), using
(119−13, 119, large)-Net in Base 4 — Upper bound on s
There is no (106, 119, large)-net in base 4, because
- 11 times m-reduction [i] would yield (106, 108, large)-net in base 4, but