Best Known (41, 41+3, s)-Nets in Base 27
(41, 41+3, large)-Net over F27 — Constructive and digital
Digital (41, 44, large)-net over F27, using
- t-expansion [i] based on digital (40, 44, large)-net over F27, using
- 3 times m-reduction [i] based on digital (40, 47, large)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 0, 532899)-net over F27, using
- s-reduction based on digital (0, 0, s)-net over F27 with arbitrarily large s, using
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 0, 532899)-net over F27 (see above)
- digital (0, 1, 532899)-net over F27, using
- s-reduction based on digital (0, 1, s)-net over F27 with arbitrarily large s, using
- digital (0, 1, 532899)-net over F27 (see above)
- digital (0, 1, 532899)-net over F27 (see above)
- digital (0, 1, 532899)-net over F27 (see above)
- digital (3, 5, 532899)-net over F27, using
- s-reduction based on digital (3, 5, 551881)-net over F27, using
- digital (4, 7, 532899)-net over F27, using
- net defined by OOA [i] based on linear OOA(277, 532899, F27, 3, 3) (dual of [(532899, 3), 1598690, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(277, 532899, F27, 2, 3) (dual of [(532899, 2), 1065791, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(277, 532899, F27, 3, 3) (dual of [(532899, 3), 1598690, 4]-NRT-code), using
- digital (24, 31, 2796200)-net over F27, using
- net defined by OOA [i] based on linear OOA(2731, 2796200, F27, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2731, 8388601, F27, 7) (dual of [8388601, 8388570, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(2731, large, F27, 7) (dual of [large, large−31, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2731, large, F27, 7) (dual of [large, large−31, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2731, 8388601, F27, 7) (dual of [8388601, 8388570, 8]-code), using
- net defined by OOA [i] based on linear OOA(2731, 2796200, F27, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
- digital (0, 0, 532899)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- 3 times m-reduction [i] based on digital (40, 47, large)-net over F27, using
(41, 41+3, large)-Net in Base 27 — Upper bound on s
There is no (41, 44, large)-net in base 27, because
- 1 times m-reduction [i] would yield (41, 43, large)-net in base 27, but