Best Known (78, 78+19, s)-Nets in Base 9
(78, 78+19, 59049)-Net over F9 — Constructive and digital
Digital (78, 97, 59049)-net over F9, using
- net defined by OOA [i] based on linear OOA(997, 59049, F9, 19, 19) (dual of [(59049, 19), 1121834, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(997, 531442, F9, 19) (dual of [531442, 531345, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 531442 | 912−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(997, 531442, F9, 19) (dual of [531442, 531345, 20]-code), using
(78, 78+19, 265721)-Net over F9 — Digital
Digital (78, 97, 265721)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(997, 265721, F9, 2, 19) (dual of [(265721, 2), 531345, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(997, 531442, F9, 19) (dual of [531442, 531345, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 531442 | 912−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- OOA 2-folding [i] based on linear OA(997, 531442, F9, 19) (dual of [531442, 531345, 20]-code), using
(78, 78+19, large)-Net in Base 9 — Upper bound on s
There is no (78, 97, large)-net in base 9, because
- 17 times m-reduction [i] would yield (78, 80, large)-net in base 9, but