Best Known (76, 102, s)-Nets in Base 9
(76, 102, 1009)-Net over F9 — Constructive and digital
Digital (76, 102, 1009)-net over F9, using
- net defined by OOA [i] based on linear OOA(9102, 1009, F9, 26, 26) (dual of [(1009, 26), 26132, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(9102, 13117, F9, 26) (dual of [13117, 13015, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9102, 13122, F9, 26) (dual of [13122, 13020, 27]-code), using
- trace code [i] based on linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- trace code [i] based on linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9102, 13122, F9, 26) (dual of [13122, 13020, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(9102, 13117, F9, 26) (dual of [13117, 13015, 27]-code), using
(76, 102, 12693)-Net over F9 — Digital
Digital (76, 102, 12693)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9102, 12693, F9, 26) (dual of [12693, 12591, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9102, 13122, F9, 26) (dual of [13122, 13020, 27]-code), using
- trace code [i] based on linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- trace code [i] based on linear OA(8151, 6561, F81, 26) (dual of [6561, 6510, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9102, 13122, F9, 26) (dual of [13122, 13020, 27]-code), using
(76, 102, large)-Net in Base 9 — Upper bound on s
There is no (76, 102, large)-net in base 9, because
- 24 times m-reduction [i] would yield (76, 78, large)-net in base 9, but