Best Known (130, 130+17, s)-Nets in Base 4
(130, 130+17, 1048575)-Net over F4 — Constructive and digital
Digital (130, 147, 1048575)-net over F4, using
- 42 times duplication [i] based on 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
(130, 130+17, 3467021)-Net over F4 — Digital
Digital (130, 147, 3467021)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4147, 3467021, F4, 2, 17) (dual of [(3467021, 2), 6933895, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4147, 4194302, F4, 2, 17) (dual of [(4194302, 2), 8388457, 18]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4145, 4194301, F4, 2, 17) (dual of [(4194301, 2), 8388457, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4145, 8388602, F4, 17) (dual of [8388602, 8388457, 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 2-folding [i] based on linear OA(4145, 8388602, F4, 17) (dual of [8388602, 8388457, 18]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4145, 4194301, F4, 2, 17) (dual of [(4194301, 2), 8388457, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4147, 4194302, F4, 2, 17) (dual of [(4194302, 2), 8388457, 18]-NRT-code), using
(130, 130+17, large)-Net in Base 4 — Upper bound on s
There is no (130, 147, large)-net in base 4, because
- 15 times m-reduction [i] would yield (130, 132, large)-net in base 4, but