Best Known (89−14, 89, s)-Nets in Base 9
(89−14, 89, 683285)-Net over F9 — Constructive and digital
Digital (75, 89, 683285)-net over F9, using
- net defined by OOA [i] based on linear OOA(989, 683285, F9, 14, 14) (dual of [(683285, 14), 9565901, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(989, 4782995, F9, 14) (dual of [4782995, 4782906, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(989, 4783001, F9, 14) (dual of [4783001, 4782912, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- 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(94, 32, F9, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,9)), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(989, 4783001, F9, 14) (dual of [4783001, 4782912, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(989, 4782995, F9, 14) (dual of [4782995, 4782906, 15]-code), using
(89−14, 89, 4783001)-Net over F9 — Digital
Digital (75, 89, 4783001)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(989, 4783001, F9, 14) (dual of [4783001, 4782912, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- 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(94, 32, F9, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,9)), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
(89−14, 89, large)-Net in Base 9 — Upper bound on s
There is no (75, 89, large)-net in base 9, because
- 12 times m-reduction [i] would yield (75, 77, large)-net in base 9, but