Best Known (47, 47+10, s)-Nets in Base 9
(47, 47+10, 956593)-Net over F9 — Constructive and digital
Digital (47, 57, 956593)-net over F9, using
- net defined by OOA [i] based on linear OOA(957, 956593, F9, 10, 10) (dual of [(956593, 10), 9565873, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(957, 4782965, F9, 10) (dual of [4782965, 4782908, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(957, 4782965, F9, 10) (dual of [4782965, 4782908, 11]-code), using
(47, 47+10, 2391484)-Net over F9 — Digital
Digital (47, 57, 2391484)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(957, 2391484, F9, 2, 10) (dual of [(2391484, 2), 4782911, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(957, 4782968, F9, 10) (dual of [4782968, 4782911, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using
- OOA 2-folding [i] based on linear OA(957, 4782968, F9, 10) (dual of [4782968, 4782911, 11]-code), using
(47, 47+10, large)-Net in Base 9 — Upper bound on s
There is no (47, 57, large)-net in base 9, because
- 8 times m-reduction [i] would yield (47, 49, large)-net in base 9, but