Best Known (218−25, 218, s)-Nets in Base 4
(218−25, 218, 699050)-Net over F4 — Constructive and digital
Digital (193, 218, 699050)-net over F4, using
- 41 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
(218−25, 218, 2796201)-Net over F4 — Digital
Digital (193, 218, 2796201)-net over F4, using
- 41 times duplication [i] based on digital (192, 217, 2796201)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4217, 2796201, F4, 3, 25) (dual of [(2796201, 3), 8388386, 26]-NRT-code), using
- OOA 3-folding [i] 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]
- OOA 3-folding [i] based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4217, 2796201, F4, 3, 25) (dual of [(2796201, 3), 8388386, 26]-NRT-code), using
(218−25, 218, large)-Net in Base 4 — Upper bound on s
There is no (193, 218, large)-net in base 4, because
- 23 times m-reduction [i] would yield (193, 195, large)-net in base 4, but