Best Known (104−19, 104, s)-Nets in Base 9
(104−19, 104, 59053)-Net over F9 — Constructive and digital
Digital (85, 104, 59053)-net over F9, using
- net defined by OOA [i] based on linear OOA(9104, 59053, F9, 19, 19) (dual of [(59053, 19), 1121903, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(9104, 531478, F9, 19) (dual of [531478, 531374, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(997, 531441, F9, 19) (dual of [531441, 531344, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(967, 531441, F9, 13) (dual of [531441, 531374, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(18) ⊂ Ce(12) [i] based on
- OOA 9-folding and stacking with additional row [i] based on linear OA(9104, 531478, F9, 19) (dual of [531478, 531374, 20]-code), using
(104−19, 104, 531478)-Net over F9 — Digital
Digital (85, 104, 531478)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9104, 531478, F9, 19) (dual of [531478, 531374, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(997, 531441, F9, 19) (dual of [531441, 531344, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(967, 531441, F9, 13) (dual of [531441, 531374, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(18) ⊂ Ce(12) [i] based on
(104−19, 104, large)-Net in Base 9 — Upper bound on s
There is no (85, 104, large)-net in base 9, because
- 17 times m-reduction [i] would yield (85, 87, large)-net in base 9, but