Best Known (95−21, 95, s)-Nets in Base 9
(95−21, 95, 5906)-Net over F9 — Constructive and digital
Digital (74, 95, 5906)-net over F9, using
- 93 times duplication [i] based on digital (71, 92, 5906)-net over F9, using
- net defined by OOA [i] based on linear OOA(992, 5906, F9, 21, 21) (dual of [(5906, 21), 123934, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(992, 59061, F9, 21) (dual of [59061, 58969, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(991, 59050, F9, 21) (dual of [59050, 58959, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(981, 59050, F9, 19) (dual of [59050, 58969, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050 | 910−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(91, 11, F9, 1) (dual of [11, 10, 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 C([0,10]) ⊂ C([0,9]) [i] based on
- OOA 10-folding and stacking with additional row [i] based on linear OA(992, 59061, F9, 21) (dual of [59061, 58969, 22]-code), using
- net defined by OOA [i] based on linear OOA(992, 5906, F9, 21, 21) (dual of [(5906, 21), 123934, 22]-NRT-code), using
(95−21, 95, 52122)-Net over F9 — Digital
Digital (74, 95, 52122)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(995, 52122, F9, 21) (dual of [52122, 52027, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(995, 59068, F9, 21) (dual of [59068, 58973, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(991, 59049, F9, 21) (dual of [59049, 58958, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(976, 59049, F9, 17) (dual of [59049, 58973, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(94, 19, F9, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,9)), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(995, 59068, F9, 21) (dual of [59068, 58973, 22]-code), using
(95−21, 95, large)-Net in Base 9 — Upper bound on s
There is no (74, 95, large)-net in base 9, because
- 19 times m-reduction [i] would yield (74, 76, large)-net in base 9, but