Best Known (227−25, 227, s)-Nets in Base 4
(227−25, 227, 699050)-Net over F4 — Constructive and digital
Digital (202, 227, 699050)-net over F4, using
- 410 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
(227−25, 227, 4194306)-Net over F4 — Digital
Digital (202, 227, 4194306)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4227, 4194306, F4, 2, 25) (dual of [(4194306, 2), 8388385, 26]-NRT-code), using
- 5 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
- 5 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
(227−25, 227, large)-Net in Base 4 — Upper bound on s
There is no (202, 227, large)-net in base 4, because
- 23 times m-reduction [i] would yield (202, 204, large)-net in base 4, but