MinT - Best Known (62, 89, s)-Nets in Base 9

Best Known (62, 89, s)-Nets in Base 9

(62, 89, 740)-Net over F₉ — Constructive and digital

Digital (62, 89, 740)-net over F₉, using

3 times m-reduction [i] based on digital (62, 92, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 46, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(62, 89, 2449)-Net over F₉ — Digital

Digital (62, 89, 2449)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 89, 2040808)-Net in Base 9 — Upper bound on s

There is no (62, 89, 2040809)-net in base 9, because

1 times m-reduction [i] would yield (62, 88, 2040809)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 940462 102932 356810 429236 729751 880580 385149 387615 519052 719657 307060 711681 618236 545065 > 9⁸⁸ [i]