Best Known (176, 196, s)-Nets in Base 4
(176, 196, 838878)-Net over F4 — Constructive and digital
Digital (176, 196, 838878)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (6, 16, 18)-net over F4, using
- 2 times m-reduction [i] based on digital (6, 18, 18)-net over F4, using
- digital (160, 180, 838860)-net over F4, using
- net defined by OOA [i] based on linear OOA(4180, 838860, F4, 20, 20) (dual of [(838860, 20), 16777020, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(4180, 8388600, F4, 20) (dual of [8388600, 8388420, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(4180, 8388600, F4, 20) (dual of [8388600, 8388420, 21]-code), using
- net defined by OOA [i] based on linear OOA(4180, 838860, F4, 20, 20) (dual of [(838860, 20), 16777020, 21]-NRT-code), using
- digital (6, 16, 18)-net over F4, using
(176, 196, 8381556)-Net over F4 — Digital
Digital (176, 196, 8381556)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4196, 8381556, F4, 20) (dual of [8381556, 8381360, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4196, large, F4, 20) (dual of [large, large−196, 21]-code), using
- 16 times code embedding in larger space [i] based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 16 times code embedding in larger space [i] based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4196, large, F4, 20) (dual of [large, large−196, 21]-code), using
(176, 196, large)-Net in Base 4 — Upper bound on s
There is no (176, 196, large)-net in base 4, because
- 18 times m-reduction [i] would yield (176, 178, large)-net in base 4, but