Best Known (198, 198+25, s)-Nets in Base 4
(198, 198+25, 699050)-Net over F4 — Constructive and digital
Digital (198, 223, 699050)-net over F4, using
- 46 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
(198, 198+25, 3370512)-Net over F4 — Digital
Digital (198, 223, 3370512)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4223, 3370512, F4, 2, 25) (dual of [(3370512, 2), 6740801, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4223, 4194304, F4, 2, 25) (dual of [(4194304, 2), 8388385, 26]-NRT-code), using
- 3 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
- 3 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(4223, 4194304, F4, 2, 25) (dual of [(4194304, 2), 8388385, 26]-NRT-code), using
(198, 198+25, large)-Net in Base 4 — Upper bound on s
There is no (198, 223, large)-net in base 4, because
- 23 times m-reduction [i] would yield (198, 200, large)-net in base 4, but