Best Known (99, 99+18, s)-Nets in Base 9
(99, 99+18, 531444)-Net over F9 — Constructive and digital
Digital (99, 117, 531444)-net over F9, using
- net defined by OOA [i] based on linear OOA(9117, 531444, F9, 18, 18) (dual of [(531444, 18), 9565875, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(9117, 4782996, F9, 18) (dual of [4782996, 4782879, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(9117, 4783001, F9, 18) (dual of [4783001, 4782884, 19]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(94, 32, F9, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,9)), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(9117, 4783001, F9, 18) (dual of [4783001, 4782884, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(9117, 4782996, F9, 18) (dual of [4782996, 4782879, 19]-code), using
(99, 99+18, 4783001)-Net over F9 — Digital
Digital (99, 117, 4783001)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9117, 4783001, F9, 18) (dual of [4783001, 4782884, 19]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(9113, 4782969, F9, 19) (dual of [4782969, 4782856, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(94, 32, F9, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,9)), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
(99, 99+18, large)-Net in Base 9 — Upper bound on s
There is no (99, 117, large)-net in base 9, because
- 16 times m-reduction [i] would yield (99, 101, large)-net in base 9, but