Best Known (177, 177+20, s)-Nets in Base 3
(177, 177+20, 838860)-Net over F3 — Constructive and digital
Digital (177, 197, 838860)-net over F3, using
- 31 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
(177, 177+20, 2097150)-Net over F3 — Digital
Digital (177, 197, 2097150)-net over F3, using
- 31 times duplication [i] based on digital (176, 196, 2097150)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3196, 2097150, F3, 4, 20) (dual of [(2097150, 4), 8388404, 21]-NRT-code), using
- OOA 4-folding [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
- OOA 4-folding [i] based on linear OA(3196, 8388600, F3, 20) (dual of [8388600, 8388404, 21]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3196, 2097150, F3, 4, 20) (dual of [(2097150, 4), 8388404, 21]-NRT-code), using
(177, 177+20, large)-Net in Base 3 — Upper bound on s
There is no (177, 197, large)-net in base 3, because
- 18 times m-reduction [i] would yield (177, 179, large)-net in base 3, but