Best Known (200, 225, s)-Nets in Base 4
(200, 225, 699050)-Net over F4 — Constructive and digital
Digital (200, 225, 699050)-net over F4, using
- 48 times duplication [i] based on digital (192, 217, 699050)-net over F4, using
- net defined by OOA [i] based on linear OOA(4217, 699050, F4, 25, 25) (dual of [(699050, 25), 17476033, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4217, 8388601, F4, 25) (dual of [8388601, 8388384, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4217, 8388601, F4, 25) (dual of [8388601, 8388384, 26]-code), using
- net defined by OOA [i] based on linear OOA(4217, 699050, F4, 25, 25) (dual of [(699050, 25), 17476033, 26]-NRT-code), using
(200, 225, 3823216)-Net over F4 — Digital
Digital (200, 225, 3823216)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4225, 3823216, F4, 2, 25) (dual of [(3823216, 2), 7646207, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4225, 4194305, F4, 2, 25) (dual of [(4194305, 2), 8388385, 26]-NRT-code), using
- 4 times NRT-code embedding in larger space [i] based on linear OOA(4217, 4194301, F4, 2, 25) (dual of [(4194301, 2), 8388385, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4217, 8388602, F4, 25) (dual of [8388602, 8388385, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- OOA 2-folding [i] based on linear OA(4217, 8388602, F4, 25) (dual of [8388602, 8388385, 26]-code), using
- 4 times NRT-code embedding in larger space [i] based on linear OOA(4217, 4194301, F4, 2, 25) (dual of [(4194301, 2), 8388385, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4225, 4194305, F4, 2, 25) (dual of [(4194305, 2), 8388385, 26]-NRT-code), using
(200, 225, large)-Net in Base 4 — Upper bound on s
There is no (200, 225, large)-net in base 4, because
- 23 times m-reduction [i] would yield (200, 202, large)-net in base 4, but