MinT - Best Known (9, 70, s)-Nets in Base 8

Best Known (9, 70, s)-Nets in Base 8

(9, 70, 45)-Net over F₈ — Constructive and digital

Digital (9, 70, 45)-net over F₈, using

net from sequence [i] based on digital (9, 44)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
  - an explicitly constructive algebraic function field [i]

(9, 70, 84)-Net in Base 8 — Upper bound on s

There is no (9, 70, 85)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁷⁰, 85, S₈, 61), but
- the linear programming bound shows that MÂ â‰¥ 487 249926 689853 563463 215557 704028 606961 141837 820881 816305 666703 085449 248768 / 198222 929395 > 8⁷⁰ [i]