Best Known (49, 59, s)-Nets in Base 9
(49, 59, 956595)-Net over F9 — Constructive and digital
Digital (49, 59, 956595)-net over F9, using
- 91 times duplication [i] based on digital (48, 58, 956595)-net over F9, using
- net defined by OOA [i] based on linear OOA(958, 956595, F9, 10, 10) (dual of [(956595, 10), 9565892, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(958, 4782975, F9, 10) (dual of [4782975, 4782917, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(958, 4782977, F9, 10) (dual of [4782977, 4782919, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(7) [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]
- linear OA(950, 4782969, F9, 8) (dual of [4782969, 4782919, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(91, 8, F9, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(958, 4782977, F9, 10) (dual of [4782977, 4782919, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(958, 4782975, F9, 10) (dual of [4782975, 4782917, 11]-code), using
- net defined by OOA [i] based on linear OOA(958, 956595, F9, 10, 10) (dual of [(956595, 10), 9565892, 11]-NRT-code), using
(49, 59, 3898144)-Net over F9 — Digital
Digital (49, 59, 3898144)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(959, 3898144, F9, 10) (dual of [3898144, 3898085, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(959, 4782979, F9, 10) (dual of [4782979, 4782920, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [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]
- linear OA(943, 4782969, F9, 7) (dual of [4782969, 4782926, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(92, 10, F9, 2) (dual of [10, 8, 3]-code or 10-arc in PG(1,9)), using
- extended Reed–Solomon code RSe(8,9) [i]
- Hamming code H(2,9) [i]
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(959, 4782979, F9, 10) (dual of [4782979, 4782920, 11]-code), using
(49, 59, large)-Net in Base 9 — Upper bound on s
There is no (49, 59, large)-net in base 9, because
- 8 times m-reduction [i] would yield (49, 51, large)-net in base 9, but