Best Known (75−12, 75, s)-Nets in Base 9
(75−12, 75, 797165)-Net over F9 — Constructive and digital
Digital (63, 75, 797165)-net over F9, using
- net defined by OOA [i] based on linear OOA(975, 797165, F9, 12, 12) (dual of [(797165, 12), 9565905, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(975, 4782990, F9, 12) (dual of [4782990, 4782915, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(975, 4782994, F9, 12) (dual of [4782994, 4782919, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(94, 25, F9, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,9)), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- discarding factors / shortening the dual code based on linear OA(975, 4782994, F9, 12) (dual of [4782994, 4782919, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(975, 4782990, F9, 12) (dual of [4782990, 4782915, 13]-code), using
(75−12, 75, 4782994)-Net over F9 — Digital
Digital (63, 75, 4782994)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(975, 4782994, F9, 12) (dual of [4782994, 4782919, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(94, 25, F9, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,9)), using
- construction X applied to Ce(11) ⊂ Ce(7) [i] based on
(75−12, 75, large)-Net in Base 9 — Upper bound on s
There is no (63, 75, large)-net in base 9, because
- 10 times m-reduction [i] would yield (63, 65, large)-net in base 9, but