Best Known (90, 90+26, s)-Nets in Base 9
(90, 90+26, 4542)-Net over F9 — Constructive and digital
Digital (90, 116, 4542)-net over F9, using
- net defined by OOA [i] based on linear OOA(9116, 4542, F9, 26, 26) (dual of [(4542, 26), 117976, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(9116, 59046, F9, 26) (dual of [59046, 58930, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9116, 59049, F9, 26) (dual of [59049, 58933, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(9116, 59049, F9, 26) (dual of [59049, 58933, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(9116, 59046, F9, 26) (dual of [59046, 58930, 27]-code), using
(90, 90+26, 45767)-Net over F9 — Digital
Digital (90, 116, 45767)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9116, 45767, F9, 26) (dual of [45767, 45651, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9116, 59049, F9, 26) (dual of [59049, 58933, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(9116, 59049, F9, 26) (dual of [59049, 58933, 27]-code), using
(90, 90+26, large)-Net in Base 9 — Upper bound on s
There is no (90, 116, large)-net in base 9, because
- 24 times m-reduction [i] would yield (90, 92, large)-net in base 9, but