Best Known (48−11, 48, s)-Nets in Base 9
(48−11, 48, 11811)-Net over F9 — Constructive and digital
Digital (37, 48, 11811)-net over F9, using
- net defined by OOA [i] based on linear OOA(948, 11811, F9, 11, 11) (dual of [(11811, 11), 129873, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(948, 59056, F9, 11) (dual of [59056, 59008, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(948, 59059, F9, 11) (dual of [59059, 59011, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(946, 59049, F9, 11) (dual of [59049, 59003, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(936, 59049, F9, 8) (dual of [59049, 59013, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, 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(948, 59059, F9, 11) (dual of [59059, 59011, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(948, 59056, F9, 11) (dual of [59056, 59008, 12]-code), using
(48−11, 48, 49876)-Net over F9 — Digital
Digital (37, 48, 49876)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(948, 49876, F9, 11) (dual of [49876, 49828, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(948, 59059, F9, 11) (dual of [59059, 59011, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(946, 59049, F9, 11) (dual of [59049, 59003, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(936, 59049, F9, 8) (dual of [59049, 59013, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, 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(948, 59059, F9, 11) (dual of [59059, 59011, 12]-code), using
(48−11, 48, large)-Net in Base 9 — Upper bound on s
There is no (37, 48, large)-net in base 9, because
- 9 times m-reduction [i] would yield (37, 39, large)-net in base 9, but