Best Known (90, 109, s)-Nets in Base 9
(90, 109, 59077)-Net over F9 — Constructive and digital
Digital (90, 109, 59077)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (3, 12, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- 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
- net defined by OOA [i] based on linear OOA(997, 59049, F9, 19, 19) (dual of [(59049, 19), 1121834, 20]-NRT-code), using
- digital (3, 12, 28)-net over F9, using
(90, 109, 566912)-Net over F9 — Digital
Digital (90, 109, 566912)-net over F9, using
(90, 109, large)-Net in Base 9 — Upper bound on s
There is no (90, 109, large)-net in base 9, because
- 17 times m-reduction [i] would yield (90, 92, large)-net in base 9, but