Best Known (186, 186+22, s)-Nets in Base 4
(186, 186+22, 762615)-Net over F4 — Constructive and digital
Digital (186, 208, 762615)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (4, 15, 15)-net over F4, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 4 and N(F) ≥ 15, using
- net from sequence [i] based on digital (4, 14)-sequence over F4, using
- 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
- digital (4, 15, 15)-net over F4, using
(186, 186+22, 4715247)-Net over F4 — Digital
Digital (186, 208, 4715247)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4208, 4715247, F4, 22) (dual of [4715247, 4715039, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4208, large, F4, 22) (dual of [large, large−208, 23]-code), using
- 15 times code embedding in larger space [i] 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]
- 15 times code embedding in larger space [i] based on linear OA(4193, large, F4, 22) (dual of [large, large−193, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4208, large, F4, 22) (dual of [large, large−208, 23]-code), using
(186, 186+22, large)-Net in Base 4 — Upper bound on s
There is no (186, 208, large)-net in base 4, because
- 20 times m-reduction [i] would yield (186, 188, large)-net in base 4, but