MinT - Best Known (65, 65+27, s)-Nets in Base 9

Best Known (65, 65+27, s)-Nets in Base 9

(65, 65+27, 740)-Net over F₉ — Constructive and digital

Digital (65, 92, 740)-net over F₉, using

6 times m-reduction [i] based on digital (65, 98, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 49, 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]

(65, 65+27, 3152)-Net over F₉ — Digital

Digital (65, 92, 3152)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+27, 3388541)-Net in Base 9 — Upper bound on s

There is no (65, 92, 3388542)-net in base 9, because

1 times m-reduction [i] would yield (65, 91, 3388542)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 685 598040 130386 481333 515887 705282 797111 642040 548365 208009 094096 410962 881493 979148 175025 > 9⁹¹ [i]