Best Known (197−22, 197, s)-Nets in Base 4
(197−22, 197, 762600)-Net over F4 — Constructive and digital
Digital (175, 197, 762600)-net over F4, using
- 44 times duplication [i] based on digital (171, 193, 762600)-net over F4, using
- net defined by OOA [i] based on linear OOA(4193, 762600, F4, 22, 22) (dual of [(762600, 22), 16777007, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(4193, 8388600, F4, 22) (dual of [8388600, 8388407, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4193, large, F4, 22) (dual of [large, large−193, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(4193, large, F4, 22) (dual of [large, large−193, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(4193, 8388600, F4, 22) (dual of [8388600, 8388407, 23]-code), using
- net defined by OOA [i] based on linear OOA(4193, 762600, F4, 22, 22) (dual of [(762600, 22), 16777007, 23]-NRT-code), using
(197−22, 197, 3991438)-Net over F4 — Digital
Digital (175, 197, 3991438)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4197, 3991438, F4, 2, 22) (dual of [(3991438, 2), 7982679, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4197, 4194303, F4, 2, 22) (dual of [(4194303, 2), 8388409, 23]-NRT-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(4193, 4194301, F4, 2, 22) (dual of [(4194301, 2), 8388409, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4193, 8388602, F4, 22) (dual of [8388602, 8388409, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4193, large, F4, 22) (dual of [large, large−193, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(4193, large, F4, 22) (dual of [large, large−193, 23]-code), using
- OOA 2-folding [i] based on linear OA(4193, 8388602, F4, 22) (dual of [8388602, 8388409, 23]-code), using
- 2 times NRT-code embedding in larger space [i] based on linear OOA(4193, 4194301, F4, 2, 22) (dual of [(4194301, 2), 8388409, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4197, 4194303, F4, 2, 22) (dual of [(4194303, 2), 8388409, 23]-NRT-code), using
(197−22, 197, large)-Net in Base 4 — Upper bound on s
There is no (175, 197, large)-net in base 4, because
- 20 times m-reduction [i] would yield (175, 177, large)-net in base 4, but