Best Known (34−5, 34, s)-Nets in Base 9
(34−5, 34, 8388602)-Net over F9 — Constructive and digital
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
(34−5, 34, large)-Net over F9 — Digital
Digital (29, 34, large)-net over F9, using
- 92 times duplication [i] based on digital (27, 32, large)-net over F9, using
(34−5, 34, large)-Net in Base 9 — Upper bound on s
There is no (29, 34, large)-net in base 9, because
- 3 times m-reduction [i] would yield (29, 31, large)-net in base 9, but