Best Known (120, 146, s)-Nets in Base 9
(120, 146, 40883)-Net over F9 — Constructive and digital
Digital (120, 146, 40883)-net over F9, using
- net defined by OOA [i] based on linear OOA(9146, 40883, F9, 26, 26) (dual of [(40883, 26), 1062812, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(9146, 531479, F9, 26) (dual of [531479, 531333, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9146, 531484, F9, 26) (dual of [531484, 531338, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(9139, 531441, F9, 26) (dual of [531441, 531302, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(97, 43, F9, 5) (dual of [43, 36, 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 Ce(25) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(9146, 531484, F9, 26) (dual of [531484, 531338, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(9146, 531479, F9, 26) (dual of [531479, 531333, 27]-code), using
(120, 146, 531484)-Net over F9 — Digital
Digital (120, 146, 531484)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9146, 531484, F9, 26) (dual of [531484, 531338, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(9139, 531441, F9, 26) (dual of [531441, 531302, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(97, 43, F9, 5) (dual of [43, 36, 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 Ce(25) ⊂ Ce(19) [i] based on
(120, 146, large)-Net in Base 9 — Upper bound on s
There is no (120, 146, large)-net in base 9, because
- 24 times m-reduction [i] would yield (120, 122, large)-net in base 9, but