Best Known (78, 101, s)-Nets in Base 9
(78, 101, 5368)-Net over F9 — Constructive and digital
Digital (78, 101, 5368)-net over F9, using
- net defined by OOA [i] based on linear OOA(9101, 5368, F9, 23, 23) (dual of [(5368, 23), 123363, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(9101, 59049, F9, 23) (dual of [59049, 58948, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- OOA 11-folding and stacking with additional row [i] based on linear OA(9101, 59049, F9, 23) (dual of [59049, 58948, 24]-code), using
(78, 101, 37956)-Net over F9 — Digital
Digital (78, 101, 37956)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9101, 37956, F9, 23) (dual of [37956, 37855, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(9101, 59049, F9, 23) (dual of [59049, 58948, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(9101, 59049, F9, 23) (dual of [59049, 58948, 24]-code), using
(78, 101, large)-Net in Base 9 — Upper bound on s
There is no (78, 101, large)-net in base 9, because
- 21 times m-reduction [i] would yield (78, 80, large)-net in base 9, but