Best Known (32, 32+5, s)-Nets in Base 9
(32, 32+5, large)-Net over F9 — Constructive and digital
Digital (32, 37, large)-net over F9, using
- 91 times duplication [i] based on digital (31, 36, large)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (0, 2, 10)-net over F9, using
- digital (29, 34, 8388602)-net over F9, using
- trace code for nets [i] based on digital (12, 17, 4194301)-net over F81, using
- net defined by OOA [i] based on linear OOA(8117, 4194301, F81, 5, 5) (dual of [(4194301, 5), 20971488, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(8117, 4194301, F81, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(8117, large, F81, 5) (dual of [large, large−17, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(8117, large, F81, 5) (dual of [large, large−17, 6]-code), using
- appending kth column [i] based on linear OOA(8117, 4194301, F81, 4, 5) (dual of [(4194301, 4), 16777187, 6]-NRT-code), using
- net defined by OOA [i] based on linear OOA(8117, 4194301, F81, 5, 5) (dual of [(4194301, 5), 20971488, 6]-NRT-code), using
- trace code for nets [i] based on digital (12, 17, 4194301)-net over F81, using
- (u, u+v)-construction [i] based on
(32, 32+5, large)-Net in Base 9 — Upper bound on s
There is no (32, 37, large)-net in base 9, because
- 3 times m-reduction [i] would yield (32, 34, large)-net in base 9, but