MinT - Best Known (70, 70+49, s)-Nets in Base 9

Best Known (70, 70+49, s)-Nets in Base 9

(70, 70+49, 344)-Net over F₉ — Constructive and digital

Digital (70, 119, 344)-net over F₉, using

7 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]

(70, 70+49, 547)-Net over F₉ — Digital

Digital (70, 119, 547)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+49, 60236)-Net in Base 9 — Upper bound on s

There is no (70, 119, 60237)-net in base 9, because

1 times m-reduction [i] would yield (70, 118, 60237)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39873 334823 588760 930818 635853 616609 476492 548245 701306 825627 993322 257089 829673 020588 023197 791779 228996 523960 733889 > 9¹¹⁸ [i]