Best Known (99−12, 99, s)-Nets in Base 4
(99−12, 99, 699050)-Net over F4 — Constructive and digital
Digital (87, 99, 699050)-net over F4, using
- net defined by OOA [i] based on linear OOA(499, 699050, F4, 12, 12) (dual of [(699050, 12), 8388501, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(499, 4194300, F4, 12) (dual of [4194300, 4194201, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(499, 4194303, F4, 12) (dual of [4194303, 4194204, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(499, 4194303, F4, 12) (dual of [4194303, 4194204, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(499, 4194300, F4, 12) (dual of [4194300, 4194201, 13]-code), using
(99−12, 99, 2097151)-Net over F4 — Digital
Digital (87, 99, 2097151)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(499, 2097151, F4, 2, 12) (dual of [(2097151, 2), 4194203, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(499, 4194302, F4, 12) (dual of [4194302, 4194203, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(499, 4194303, F4, 12) (dual of [4194303, 4194204, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(499, 4194303, F4, 12) (dual of [4194303, 4194204, 13]-code), using
- OOA 2-folding [i] based on linear OA(499, 4194302, F4, 12) (dual of [4194302, 4194203, 13]-code), using
(99−12, 99, large)-Net in Base 4 — Upper bound on s
There is no (87, 99, large)-net in base 4, because
- 10 times m-reduction [i] would yield (87, 89, large)-net in base 4, but