Best Known (89, 89+17, s)-Nets in Base 9
(89, 89+17, 597871)-Net over F9 — Constructive and digital
Digital (89, 106, 597871)-net over F9, using
- net defined by OOA [i] based on linear OOA(9106, 597871, F9, 17, 17) (dual of [(597871, 17), 10163701, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using
(89, 89+17, 3840372)-Net over F9 — Digital
Digital (89, 106, 3840372)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9106, 3840372, F9, 17) (dual of [3840372, 3840266, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using
(89, 89+17, large)-Net in Base 9 — Upper bound on s
There is no (89, 106, large)-net in base 9, because
- 15 times m-reduction [i] would yield (89, 91, large)-net in base 9, but