Best Known (35, 35+8, s)-Nets in Base 9
(35, 35+8, 132861)-Net over F9 — Constructive and digital
Digital (35, 43, 132861)-net over F9, using
- net defined by OOA [i] based on linear OOA(943, 132861, F9, 8, 8) (dual of [(132861, 8), 1062845, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(943, 531444, F9, 8) (dual of [531444, 531401, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(943, 531447, F9, 8) (dual of [531447, 531404, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(943, 531441, F9, 8) (dual of [531441, 531398, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(937, 531441, F9, 7) (dual of [531441, 531404, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(90, 6, F9, 0) (dual of [6, 6, 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
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(943, 531447, F9, 8) (dual of [531447, 531404, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(943, 531444, F9, 8) (dual of [531444, 531401, 9]-code), using
(35, 35+8, 531447)-Net over F9 — Digital
Digital (35, 43, 531447)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(943, 531447, F9, 8) (dual of [531447, 531404, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(943, 531441, F9, 8) (dual of [531441, 531398, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(937, 531441, F9, 7) (dual of [531441, 531404, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(90, 6, F9, 0) (dual of [6, 6, 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
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
(35, 35+8, large)-Net in Base 9 — Upper bound on s
There is no (35, 43, large)-net in base 9, because
- 6 times m-reduction [i] would yield (35, 37, large)-net in base 9, but