Best Known (186, 186+20, s)-Nets in Base 3
(186, 186+20, 838864)-Net over F3 — Constructive and digital
Digital (186, 206, 838864)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 4)-net over F3, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- 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
- digital (0, 10, 4)-net over F3, using
(186, 186+20, 2796205)-Net over F3 — Digital
Digital (186, 206, 2796205)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3206, 2796205, F3, 3, 20) (dual of [(2796205, 3), 8388409, 21]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(310, 4, F3, 3, 10) (dual of [(4, 3), 2, 11]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;2,3) [i]
- 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
- linear OOA(310, 4, F3, 3, 10) (dual of [(4, 3), 2, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
(186, 186+20, large)-Net in Base 3 — Upper bound on s
There is no (186, 206, large)-net in base 3, because
- 18 times m-reduction [i] would yield (186, 188, large)-net in base 3, but