Best Known (181, 181+20, s)-Nets in Base 3
(181, 181+20, 838860)-Net over F3 — Constructive and digital
Digital (181, 201, 838860)-net over F3, using
- 35 times duplication [i] based on digital (176, 196, 838860)-net over F3, using
- net defined by OOA [i] based on linear OOA(3196, 838860, F3, 20, 20) (dual of [(838860, 20), 16777004, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(3196, 8388600, F3, 20) (dual of [8388600, 8388404, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(3196, 8388600, F3, 20) (dual of [8388600, 8388404, 21]-code), using
- net defined by OOA [i] based on linear OOA(3196, 838860, F3, 20, 20) (dual of [(838860, 20), 16777004, 21]-NRT-code), using
(181, 181+20, 2728236)-Net over F3 — Digital
Digital (181, 201, 2728236)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3201, 2728236, F3, 3, 20) (dual of [(2728236, 3), 8184507, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3201, 2796202, F3, 3, 20) (dual of [(2796202, 3), 8388405, 21]-NRT-code), using
- 32 times duplication [i] based on linear OOA(3199, 2796202, F3, 3, 20) (dual of [(2796202, 3), 8388407, 21]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3196, 2796201, F3, 3, 20) (dual of [(2796201, 3), 8388407, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- OOA 3-folding [i] based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3196, 2796201, F3, 3, 20) (dual of [(2796201, 3), 8388407, 21]-NRT-code), using
- 32 times duplication [i] based on linear OOA(3199, 2796202, F3, 3, 20) (dual of [(2796202, 3), 8388407, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3201, 2796202, F3, 3, 20) (dual of [(2796202, 3), 8388405, 21]-NRT-code), using
(181, 181+20, large)-Net in Base 3 — Upper bound on s
There is no (181, 201, large)-net in base 3, because
- 18 times m-reduction [i] would yield (181, 183, large)-net in base 3, but