MinT - Best Known (81−28, 81, s)-Nets in Base 9

Best Known (81−28, 81, s)-Nets in Base 9

(81−28, 81, 344)-Net over F₉ — Constructive and digital

Digital (53, 81, 344)-net over F₉, using

11 times m-reduction [i] based on digital (53, 92, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 46, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(81−28, 81, 1009)-Net over F₉ — Digital

Digital (53, 81, 1009)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(81−28, 81, 250800)-Net in Base 9 — Upper bound on s

There is no (53, 81, 250801)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 196635 151367 670371 496886 670871 183426 707524 922463 753754 049798 012580 175690 322481 > 9⁸¹ [i]