Best Known (61−12, 61, s)-Nets in Base 9
(61−12, 61, 88574)-Net over F9 — Constructive and digital
Digital (49, 61, 88574)-net over F9, using
- net defined by OOA [i] based on linear OOA(961, 88574, F9, 12, 12) (dual of [(88574, 12), 1062827, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(961, 531444, F9, 12) (dual of [531444, 531383, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(961, 531447, F9, 12) (dual of [531447, 531386, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(961, 531441, F9, 12) (dual of [531441, 531380, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(955, 531441, F9, 11) (dual of [531441, 531386, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(961, 531447, F9, 12) (dual of [531447, 531386, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(961, 531444, F9, 12) (dual of [531444, 531383, 13]-code), using
(61−12, 61, 300839)-Net over F9 — Digital
Digital (49, 61, 300839)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(961, 300839, F9, 12) (dual of [300839, 300778, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(961, 531441, F9, 12) (dual of [531441, 531380, 13]-code), using
- an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(961, 531441, F9, 12) (dual of [531441, 531380, 13]-code), using
(61−12, 61, large)-Net in Base 9 — Upper bound on s
There is no (49, 61, large)-net in base 9, because
- 10 times m-reduction [i] would yield (49, 51, large)-net in base 9, but