Best Known (38, 45, s)-Nets in Base 9
(38, 45, 1594328)-Net over F9 — Constructive and digital
Digital (38, 45, 1594328)-net over F9, using
- 91 times duplication [i] based on digital (37, 44, 1594328)-net over F9, using
- net defined by OOA [i] based on linear OOA(944, 1594328, F9, 7, 7) (dual of [(1594328, 7), 11160252, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(944, 4782985, F9, 7) (dual of [4782985, 4782941, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(943, 4782970, F9, 7) (dual of [4782970, 4782927, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(929, 4782970, F9, 5) (dual of [4782970, 4782941, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 914−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(91, 15, F9, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- OOA 3-folding and stacking with additional row [i] based on linear OA(944, 4782985, F9, 7) (dual of [4782985, 4782941, 8]-code), using
- net defined by OOA [i] based on linear OOA(944, 1594328, F9, 7, 7) (dual of [(1594328, 7), 11160252, 8]-NRT-code), using
(38, 45, 5369714)-Net over F9 — Digital
Digital (38, 45, 5369714)-net over F9, using
(38, 45, large)-Net in Base 9 — Upper bound on s
There is no (38, 45, large)-net in base 9, because
- 5 times m-reduction [i] would yield (38, 40, large)-net in base 9, but