Best Known (226−24, 226, s)-Nets in Base 4
(226−24, 226, 699050)-Net over F4 — Constructive and digital
Digital (202, 226, 699050)-net over F4, using
- 49 times duplication [i] based on digital (193, 217, 699050)-net over F4, using
- t-expansion [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
- t-expansion [i] based on digital (192, 217, 699050)-net over F4, using
(226−24, 226, 4336724)-Net over F4 — Digital
Digital (202, 226, 4336724)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4226, 4336724, F4, 24) (dual of [4336724, 4336498, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4226, large, F4, 24) (dual of [large, large−226, 25]-code), using
- 10 times code embedding in larger space [i] based on linear OA(4216, large, F4, 24) (dual of [large, large−216, 25]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 10 times code embedding in larger space [i] based on linear OA(4216, large, F4, 24) (dual of [large, large−216, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4226, large, F4, 24) (dual of [large, large−226, 25]-code), using
(226−24, 226, large)-Net in Base 4 — Upper bound on s
There is no (202, 226, large)-net in base 4, because
- 22 times m-reduction [i] would yield (202, 204, large)-net in base 4, but