Best Known (46, 46+11, s)-Nets in Base 9
(46, 46+11, 106290)-Net over F9 — Constructive and digital
Digital (46, 57, 106290)-net over F9, using
- net defined by OOA [i] based on linear OOA(957, 106290, F9, 11, 11) (dual of [(106290, 11), 1169133, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(957, 531451, F9, 11) (dual of [531451, 531394, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(955, 531441, F9, 11) (dual of [531441, 531386, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(943, 531441, F9, 8) (dual of [531441, 531398, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(10) ⊂ Ce(7) [i] based on
- OOA 5-folding and stacking with additional row [i] based on linear OA(957, 531451, F9, 11) (dual of [531451, 531394, 12]-code), using
(46, 46+11, 448917)-Net over F9 — Digital
Digital (46, 57, 448917)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(957, 448917, F9, 11) (dual of [448917, 448860, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(957, 531451, F9, 11) (dual of [531451, 531394, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(955, 531441, F9, 11) (dual of [531441, 531386, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(943, 531441, F9, 8) (dual of [531441, 531398, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(10) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(957, 531451, F9, 11) (dual of [531451, 531394, 12]-code), using
(46, 46+11, large)-Net in Base 9 — Upper bound on s
There is no (46, 57, large)-net in base 9, because
- 9 times m-reduction [i] would yield (46, 48, large)-net in base 9, but