Best Known (47, 56, s)-Nets in Base 9
(47, 56, 1195741)-Net over F9 — Constructive and digital
Digital (47, 56, 1195741)-net over F9, using
- net defined by OOA [i] based on linear OOA(956, 1195741, F9, 9, 9) (dual of [(1195741, 9), 10761613, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(956, 4782965, F9, 9) (dual of [4782965, 4782909, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(956, 4782968, F9, 9) (dual of [4782968, 4782912, 10]-code), using
- 1 times truncation [i] 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]
- 1 times truncation [i] based on linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(956, 4782968, F9, 9) (dual of [4782968, 4782912, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(956, 4782965, F9, 9) (dual of [4782965, 4782909, 10]-code), using
(47, 56, 4782968)-Net over F9 — Digital
Digital (47, 56, 4782968)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(956, 4782968, F9, 9) (dual of [4782968, 4782912, 10]-code), using
- 1 times truncation [i] 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]
- 1 times truncation [i] based on linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using
(47, 56, large)-Net in Base 9 — Upper bound on s
There is no (47, 56, large)-net in base 9, because
- 7 times m-reduction [i] would yield (47, 49, large)-net in base 9, but