MinT - Best Known (115−45, 115, s)-Nets in Base 9

Best Known (115−45, 115, s)-Nets in Base 9

(115−45, 115, 344)-Net over F₉ — Constructive and digital

Digital (70, 115, 344)-net over F₉, using

11 times m-reduction [i] based on digital (70, 126, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 63, 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]

(115−45, 115, 692)-Net over F₉ — Digital

Digital (70, 115, 692)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−45, 115, 99636)-Net in Base 9 — Upper bound on s

There is no (70, 115, 99637)-net in base 9, because

1 times m-reduction [i] would yield (70, 114, 99637)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 077678 287385 353565 958060 455665 053145 985613 857075 578592 416905 848598 621826 838482 372041 557344 610427 880021 245105 > 9¹¹⁴ [i]