Best Known (120−25, 120, s)-Nets in Base 9
(120−25, 120, 4924)-Net over F9 — Constructive and digital
Digital (95, 120, 4924)-net over F9, using
- net defined by OOA [i] based on linear OOA(9120, 4924, F9, 25, 25) (dual of [(4924, 25), 122980, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(9120, 59089, F9, 25) (dual of [59089, 58969, 26]-code), using
- 2 times code embedding in larger space [i] based on linear OA(9118, 59087, F9, 25) (dual of [59087, 58969, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(9111, 59050, F9, 25) (dual of [59050, 58939, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(981, 59050, F9, 19) (dual of [59050, 58969, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(97, 37, F9, 5) (dual of [37, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(9118, 59087, F9, 25) (dual of [59087, 58969, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(9120, 59089, F9, 25) (dual of [59089, 58969, 26]-code), using
(120−25, 120, 72370)-Net over F9 — Digital
Digital (95, 120, 72370)-net over F9, using
(120−25, 120, large)-Net in Base 9 — Upper bound on s
There is no (95, 120, large)-net in base 9, because
- 23 times m-reduction [i] would yield (95, 97, large)-net in base 9, but