Best Known (62−6, 62, s)-Nets in Base 9
(62−6, 62, large)-Net over F9 — Constructive and digital
Digital (56, 62, large)-net over F9, using
- t-expansion [i] based on digital (55, 62, large)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (9, 12, 5580100)-net over F9, using
- net defined by OOA [i] based on linear OOA(912, 5580100, F9, 3, 3) (dual of [(5580100, 3), 16740288, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(912, 5580100, F9, 2, 3) (dual of [(5580100, 2), 11160188, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(912, 5580100, F9, 3) (dual of [5580100, 5580088, 4]-code or 5580100-cap in PG(11,9)), using
- appending kth column [i] based on linear OOA(912, 5580100, F9, 2, 3) (dual of [(5580100, 2), 11160188, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(912, 5580100, F9, 3, 3) (dual of [(5580100, 3), 16740288, 4]-NRT-code), using
- digital (43, 50, 5592401)-net over F9, using
- net defined by OOA [i] based on linear OOA(950, 5592401, F9, 9, 7) (dual of [(5592401, 9), 50331559, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(950, 5592402, F9, 3, 7) (dual of [(5592402, 3), 16777156, 8]-NRT-code), using
- trace code [i] based on linear OOA(8125, 2796201, F81, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8125, large, F81, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(8125, large, F81, 7) (dual of [large, large−25, 8]-code), using
- trace code [i] based on linear OOA(8125, 2796201, F81, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(950, 5592402, F9, 3, 7) (dual of [(5592402, 3), 16777156, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(950, 5592401, F9, 9, 7) (dual of [(5592401, 9), 50331559, 8]-NRT-code), using
- digital (9, 12, 5580100)-net over F9, using
- (u, u+v)-construction [i] based on
(62−6, 62, large)-Net in Base 9 — Upper bound on s
There is no (56, 62, large)-net in base 9, because
- 4 times m-reduction [i] would yield (56, 58, large)-net in base 9, but