Best Known (92, 92+21, s)-Nets in Base 9
(92, 92+21, 53146)-Net over F9 — Constructive and digital
Digital (92, 113, 53146)-net over F9, using
- net defined by OOA [i] based on linear OOA(9113, 53146, F9, 21, 21) (dual of [(53146, 21), 1115953, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(9113, 531461, F9, 21) (dual of [531461, 531348, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(9113, 531463, F9, 21) (dual of [531463, 531350, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(9109, 531441, F9, 21) (dual of [531441, 531332, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(94, 22, F9, 3) (dual of [22, 18, 4]-code or 22-cap in PG(3,9)), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(9113, 531463, F9, 21) (dual of [531463, 531350, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(9113, 531461, F9, 21) (dual of [531461, 531348, 22]-code), using
(92, 92+21, 417948)-Net over F9 — Digital
Digital (92, 113, 417948)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9113, 417948, F9, 21) (dual of [417948, 417835, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(9113, 531463, F9, 21) (dual of [531463, 531350, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(9109, 531441, F9, 21) (dual of [531441, 531332, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(94, 22, F9, 3) (dual of [22, 18, 4]-code or 22-cap in PG(3,9)), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(9113, 531463, F9, 21) (dual of [531463, 531350, 22]-code), using
(92, 92+21, large)-Net in Base 9 — Upper bound on s
There is no (92, 113, large)-net in base 9, because
- 19 times m-reduction [i] would yield (92, 94, large)-net in base 9, but