MinT - Best Known (77, 77+36, s)-Nets in Base 9

Best Known (77, 77+36, s)-Nets in Base 9

(77, 77+36, 740)-Net over F₉ — Constructive and digital

Digital (77, 113, 740)-net over F₉, using

9 times m-reduction [i] based on digital (77, 122, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 61, 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]

(77, 77+36, 2112)-Net over F₉ — Digital

Digital (77, 113, 2112)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+36, 923756)-Net in Base 9 — Upper bound on s

There is no (77, 113, 923757)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 675163 692561 919329 162875 302886 488393 900889 253067 490213 614188 258748 244377 676559 370958 319090 331363 700733 778449 > 9¹¹³ [i]