Best Known (112, 112+25, s)-Nets in Base 9
(112, 112+25, 44289)-Net over F9 — Constructive and digital
Digital (112, 137, 44289)-net over F9, using
- net defined by OOA [i] based on linear OOA(9137, 44289, F9, 25, 25) (dual of [(44289, 25), 1107088, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(9137, 531469, F9, 25) (dual of [531469, 531332, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(9137, 531470, F9, 25) (dual of [531470, 531333, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(9133, 531442, F9, 25) (dual of [531442, 531309, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 912−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(9109, 531442, F9, 21) (dual of [531442, 531333, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 912−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(94, 28, F9, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,9)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(9137, 531470, F9, 25) (dual of [531470, 531333, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(9137, 531469, F9, 25) (dual of [531469, 531332, 26]-code), using
(112, 112+25, 517407)-Net over F9 — Digital
Digital (112, 137, 517407)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9137, 517407, F9, 25) (dual of [517407, 517270, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(9137, 531470, F9, 25) (dual of [531470, 531333, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(9133, 531442, F9, 25) (dual of [531442, 531309, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 912−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(9109, 531442, F9, 21) (dual of [531442, 531333, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 912−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(94, 28, F9, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,9)), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(9137, 531470, F9, 25) (dual of [531470, 531333, 26]-code), using
(112, 112+25, large)-Net in Base 9 — Upper bound on s
There is no (112, 137, large)-net in base 9, because
- 23 times m-reduction [i] would yield (112, 114, large)-net in base 9, but