Best Known (158−17, 158, s)-Nets in Base 4
(158−17, 158, 1048592)-Net over F4 — Constructive and digital
Digital (141, 158, 1048592)-net over F4, using
- 41 times duplication [i] based on digital (140, 157, 1048592)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (4, 12, 17)-net over F4, using
- digital (128, 145, 1048575)-net over F4, using
- net defined by OOA [i] based on linear OOA(4145, 1048575, F4, 17, 17) (dual of [(1048575, 17), 17825630, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(4145, 8388601, F4, 17) (dual of [8388601, 8388456, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(4145, 8388601, F4, 17) (dual of [8388601, 8388456, 18]-code), using
- net defined by OOA [i] based on linear OOA(4145, 1048575, F4, 17, 17) (dual of [(1048575, 17), 17825630, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
(158−17, 158, 4287513)-Net over F4 — Digital
Digital (141, 158, 4287513)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4158, 4287513, F4, 17) (dual of [4287513, 4287355, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4158, large, F4, 17) (dual of [large, large−158, 18]-code), using
- 13 times code embedding in larger space [i] based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 13 times code embedding in larger space [i] based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4158, large, F4, 17) (dual of [large, large−158, 18]-code), using
(158−17, 158, large)-Net in Base 4 — Upper bound on s
There is no (141, 158, large)-net in base 4, because
- 15 times m-reduction [i] would yield (141, 143, large)-net in base 4, but