Best Known (74, 74+17, s)-Nets in Base 9
(74, 74+17, 66430)-Net over F9 — Constructive and digital
Digital (74, 91, 66430)-net over F9, using
- net defined by OOA [i] based on linear OOA(991, 66430, F9, 17, 17) (dual of [(66430, 17), 1129219, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on 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]
- OOA 8-folding and stacking with additional row [i] based on linear OA(991, 531441, F9, 17) (dual of [531441, 531350, 18]-code), using
(74, 74+17, 426701)-Net over F9 — Digital
Digital (74, 91, 426701)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(991, 426701, F9, 17) (dual of [426701, 426610, 18]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(991, 531441, F9, 17) (dual of [531441, 531350, 18]-code), using
(74, 74+17, large)-Net in Base 9 — Upper bound on s
There is no (74, 91, large)-net in base 9, because
- 15 times m-reduction [i] would yield (74, 76, large)-net in base 9, but