MinT - Best Known (70, 70+46, s)-Nets in Base 9

Best Known (70, 70+46, s)-Nets in Base 9

(70, 70+46, 344)-Net over F₉ — Constructive and digital

Digital (70, 116, 344)-net over F₉, using

10 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+46, 650)-Net over F₉ — Digital

Digital (70, 116, 650)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+46, 76557)-Net in Base 9 — Upper bound on s

There is no (70, 116, 76558)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 492 230650 944185 132686 727445 736586 685735 726541 749261 158349 669067 737405 146285 815574 619424 676562 514416 946280 964945 > 9¹¹⁶ [i]