Best Known (216−24, 216, s)-Nets in Base 4
(216−24, 216, 699050)-Net over F4 — Constructive and digital
Digital (192, 216, 699050)-net over F4, using
- net defined by OOA [i] based on linear OOA(4216, 699050, F4, 24, 24) (dual of [(699050, 24), 16776984, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(4216, 8388600, F4, 24) (dual of [8388600, 8388384, 25]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(4216, large, F4, 24) (dual of [large, large−216, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(4216, 8388600, F4, 24) (dual of [8388600, 8388384, 25]-code), using
(216−24, 216, 3950459)-Net over F4 — Digital
Digital (192, 216, 3950459)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4216, 3950459, F4, 2, 24) (dual of [(3950459, 2), 7900702, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4216, 4194301, F4, 2, 24) (dual of [(4194301, 2), 8388386, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4216, 8388602, F4, 24) (dual of [8388602, 8388386, 25]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(4216, large, F4, 24) (dual of [large, large−216, 25]-code), using
- OOA 2-folding [i] based on linear OA(4216, 8388602, F4, 24) (dual of [8388602, 8388386, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(4216, 4194301, F4, 2, 24) (dual of [(4194301, 2), 8388386, 25]-NRT-code), using
(216−24, 216, large)-Net in Base 4 — Upper bound on s
There is no (192, 216, large)-net in base 4, because
- 22 times m-reduction [i] would yield (192, 194, large)-net in base 4, but