Best Known (70−15, 70, s)-Nets in Base 27
(70−15, 70, 76163)-Net over F27 — Constructive and digital
Digital (55, 70, 76163)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 13, 243)-net over F27, using
- net defined by OOA [i] based on linear OOA(2713, 243, F27, 7, 7) (dual of [(243, 7), 1688, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(2713, 730, F27, 7) (dual of [730, 717, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 730 | 274−1, 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(2713, 730, F27, 7) (dual of [730, 717, 8]-code), using
- net defined by OOA [i] based on linear OOA(2713, 243, F27, 7, 7) (dual of [(243, 7), 1688, 8]-NRT-code), using
- digital (42, 57, 75920)-net over F27, using
- net defined by OOA [i] based on linear OOA(2757, 75920, F27, 15, 15) (dual of [(75920, 15), 1138743, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2757, 531441, F27, 15) (dual of [531441, 531384, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 7-folding and stacking with additional row [i] based on linear OA(2757, 531441, F27, 15) (dual of [531441, 531384, 16]-code), using
- net defined by OOA [i] based on linear OOA(2757, 75920, F27, 15, 15) (dual of [(75920, 15), 1138743, 16]-NRT-code), using
- digital (6, 13, 243)-net over F27, using
(70−15, 70, 3336600)-Net over F27 — Digital
Digital (55, 70, 3336600)-net over F27, using
(70−15, 70, large)-Net in Base 27 — Upper bound on s
There is no (55, 70, large)-net in base 27, because
- 13 times m-reduction [i] would yield (55, 57, large)-net in base 27, but