Best Known (34, 34+9, s)-Nets in Base 9
(34, 34+9, 14765)-Net over F9 — Constructive and digital
Digital (34, 43, 14765)-net over F9, using
- 91 times duplication [i] based on digital (33, 42, 14765)-net over F9, using
- net defined by OOA [i] based on linear OOA(942, 14765, F9, 9, 9) (dual of [(14765, 9), 132843, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(942, 59061, F9, 9) (dual of [59061, 59019, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(941, 59050, F9, 9) (dual of [59050, 59009, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(931, 59050, F9, 7) (dual of [59050, 59019, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(91, 11, F9, 1) (dual of [11, 10, 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([0,4]) ⊂ C([0,3]) [i] based on
- OOA 4-folding and stacking with additional row [i] based on linear OA(942, 59061, F9, 9) (dual of [59061, 59019, 10]-code), using
- net defined by OOA [i] based on linear OOA(942, 14765, F9, 9, 9) (dual of [(14765, 9), 132843, 10]-NRT-code), using
(34, 34+9, 63340)-Net over F9 — Digital
Digital (34, 43, 63340)-net over F9, using
(34, 34+9, large)-Net in Base 9 — Upper bound on s
There is no (34, 43, large)-net in base 9, because
- 7 times m-reduction [i] would yield (34, 36, large)-net in base 9, but