Best Known (39, 49, s)-Nets in Base 9
(39, 49, 106288)-Net over F9 — Constructive and digital
Digital (39, 49, 106288)-net over F9, using
- net defined by OOA [i] based on linear OOA(949, 106288, F9, 10, 10) (dual of [(106288, 10), 1062831, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(949, 531440, F9, 10) (dual of [531440, 531391, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(949, 531441, F9, 10) (dual of [531441, 531392, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(949, 531441, F9, 10) (dual of [531441, 531392, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(949, 531440, F9, 10) (dual of [531440, 531391, 11]-code), using
(39, 49, 265720)-Net over F9 — Digital
Digital (39, 49, 265720)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(949, 265720, F9, 2, 10) (dual of [(265720, 2), 531391, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(949, 531440, F9, 10) (dual of [531440, 531391, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(949, 531441, F9, 10) (dual of [531441, 531392, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(949, 531441, F9, 10) (dual of [531441, 531392, 11]-code), using
- OOA 2-folding [i] based on linear OA(949, 531440, F9, 10) (dual of [531440, 531391, 11]-code), using
(39, 49, large)-Net in Base 9 — Upper bound on s
There is no (39, 49, large)-net in base 9, because
- 8 times m-reduction [i] would yield (39, 41, large)-net in base 9, but