Best Known (93−15, 93, s)-Nets in Base 27
(93−15, 93, 1204960)-Net over F27 — Constructive and digital
Digital (78, 93, 1204960)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (15, 22, 6589)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- digital (12, 19, 6561)-net over F27, using
- net defined by OOA [i] based on linear OOA(2719, 6561, F27, 7, 7) (dual of [(6561, 7), 45908, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2719, 19684, F27, 7) (dual of [19684, 19665, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- OOA 3-folding and stacking with additional row [i] based on linear OA(2719, 19684, F27, 7) (dual of [19684, 19665, 8]-code), using
- net defined by OOA [i] based on linear OOA(2719, 6561, F27, 7, 7) (dual of [(6561, 7), 45908, 8]-NRT-code), using
- digital (0, 3, 28)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (56, 71, 1198371)-net over F27, using
- net defined by OOA [i] based on linear OOA(2771, 1198371, F27, 15, 15) (dual of [(1198371, 15), 17975494, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2771, 8388598, F27, 15) (dual of [8388598, 8388527, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2771, large, F27, 15) (dual of [large, large−71, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2771, large, F27, 15) (dual of [large, large−71, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2771, 8388598, F27, 15) (dual of [8388598, 8388527, 16]-code), using
- net defined by OOA [i] based on linear OOA(2771, 1198371, F27, 15, 15) (dual of [(1198371, 15), 17975494, 16]-NRT-code), using
- digital (15, 22, 6589)-net over F27, using
(93−15, 93, large)-Net over F27 — Digital
Digital (78, 93, large)-net over F27, using
- t-expansion [i] based on digital (76, 93, large)-net over F27, using
- 3 times m-reduction [i] based on digital (76, 96, large)-net over F27, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2796, large, F27, 20) (dual of [large, large−96, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(2796, large, F27, 20) (dual of [large, large−96, 21]-code), using
- 3 times m-reduction [i] based on digital (76, 96, large)-net over F27, using
(93−15, 93, large)-Net in Base 27 — Upper bound on s
There is no (78, 93, large)-net in base 27, because
- 13 times m-reduction [i] would yield (78, 80, large)-net in base 27, but