Best Known (5, 12, s)-Nets in Base 9
(5, 12, 32)-Net over F9 — Constructive and digital
Digital (5, 12, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
(5, 12, 38)-Net in Base 9 — Constructive
(5, 12, 38)-net in base 9, using
- base change [i] based on digital (1, 8, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
(5, 12, 41)-Net over F9 — Digital
Digital (5, 12, 41)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(912, 41, F9, 2, 7) (dual of [(41, 2), 70, 8]-NRT-code), using
- OOA 2-folding [i] based on linear OA(912, 82, F9, 7) (dual of [82, 70, 8]-code), using
- a “GraNC†code from Grassl’s database [i]
- OOA 2-folding [i] based on linear OA(912, 82, F9, 7) (dual of [82, 70, 8]-code), using
(5, 12, 715)-Net in Base 9 — Upper bound on s
There is no (5, 12, 716)-net in base 9, because
- 1 times m-reduction [i] would yield (5, 11, 716)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 31503 261089 > 911 [i]