Best Known (107, 130, s)-Nets in Base 9
(107, 130, 48316)-Net over F9 — Constructive and digital
Digital (107, 130, 48316)-net over F9, using
- 92 times duplication [i] based on digital (105, 128, 48316)-net over F9, using
- net defined by OOA [i] based on linear OOA(9128, 48316, F9, 23, 23) (dual of [(48316, 23), 1111140, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(9128, 531477, F9, 23) (dual of [531477, 531349, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(9128, 531478, F9, 23) (dual of [531478, 531350, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(9121, 531441, F9, 23) (dual of [531441, 531320, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(991, 531441, F9, 17) (dual of [531441, 531350, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(22) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(9128, 531478, F9, 23) (dual of [531478, 531350, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(9128, 531477, F9, 23) (dual of [531477, 531349, 24]-code), using
- net defined by OOA [i] based on linear OOA(9128, 48316, F9, 23, 23) (dual of [(48316, 23), 1111140, 24]-NRT-code), using
(107, 130, 531482)-Net over F9 — Digital
Digital (107, 130, 531482)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9130, 531482, F9, 23) (dual of [531482, 531352, 24]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9128, 531478, F9, 23) (dual of [531478, 531350, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(16) [i] based on
- linear OA(9121, 531441, F9, 23) (dual of [531441, 531320, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(991, 531441, F9, 17) (dual of [531441, 531350, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(22) ⊂ Ce(16) [i] based on
- linear OA(9128, 531480, F9, 22) (dual of [531480, 531352, 23]-code), using Gilbert–Varšamov bound and bm = 9128 > Vbs−1(k−1) = 310159 187992 674721 341249 782712 345305 110604 196895 295574 480446 148206 538826 253829 075543 606796 631977 696003 162249 529393 571321 [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(9128, 531478, F9, 23) (dual of [531478, 531350, 24]-code), using
- construction X with Varšamov bound [i] based on
(107, 130, large)-Net in Base 9 — Upper bound on s
There is no (107, 130, large)-net in base 9, because
- 21 times m-reduction [i] would yield (107, 109, large)-net in base 9, but