Best Known (114, 114+25, s)-Nets in Base 9
(114, 114+25, 44289)-Net over F9 — Constructive and digital
Digital (114, 139, 44289)-net over F9, using
- 92 times duplication [i] based on 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
- net defined by OOA [i] based on linear OOA(9137, 44289, F9, 25, 25) (dual of [(44289, 25), 1107088, 26]-NRT-code), using
(114, 114+25, 531477)-Net over F9 — Digital
Digital (114, 139, 531477)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9139, 531477, F9, 25) (dual of [531477, 531338, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(9133, 531441, F9, 25) (dual of [531441, 531308, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(9103, 531441, F9, 20) (dual of [531441, 531338, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(96, 36, F9, 4) (dual of [36, 30, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
(114, 114+25, large)-Net in Base 9 — Upper bound on s
There is no (114, 139, large)-net in base 9, because
- 23 times m-reduction [i] would yield (114, 116, large)-net in base 9, but