Best Known (92, 112, s)-Nets in Base 9
(92, 112, 53148)-Net over F9 — Constructive and digital
Digital (92, 112, 53148)-net over F9, using
- net defined by OOA [i] based on linear OOA(9112, 53148, F9, 20, 20) (dual of [(53148, 20), 1062848, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(9112, 531480, F9, 20) (dual of [531480, 531368, 21]-code), using
- 2 times code embedding in larger space [i] based on linear OA(9110, 531478, F9, 20) (dual of [531478, 531368, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- 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(973, 531441, F9, 14) (dual of [531441, 531368, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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 Ce(19) ⊂ Ce(13) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(9110, 531478, F9, 20) (dual of [531478, 531368, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(9112, 531480, F9, 20) (dual of [531480, 531368, 21]-code), using
(92, 112, 531482)-Net over F9 — Digital
Digital (92, 112, 531482)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9112, 531482, F9, 20) (dual of [531482, 531370, 21]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9110, 531478, F9, 20) (dual of [531478, 531368, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- 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(973, 531441, F9, 14) (dual of [531441, 531368, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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 Ce(19) ⊂ Ce(13) [i] based on
- linear OA(9110, 531480, F9, 19) (dual of [531480, 531370, 20]-code), using Gilbert–Varšamov bound and bm = 9110 > Vbs−1(k−1) = 32 203681 693704 491179 264768 564467 885499 111454 960634 570281 484030 782374 745656 597106 798712 435860 718601 266681 [i]
- linear OA(90, 2, F9, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(9110, 531478, F9, 20) (dual of [531478, 531368, 21]-code), using
- construction X with Varšamov bound [i] based on
(92, 112, large)-Net in Base 9 — Upper bound on s
There is no (92, 112, large)-net in base 9, because
- 18 times m-reduction [i] would yield (92, 94, large)-net in base 9, but