MinT - Best Known (79, 79+49, s)-Nets in Base 9

Best Known (79, 79+49, s)-Nets in Base 9

(79, 79+49, 448)-Net over F₉ — Constructive and digital

Digital (79, 128, 448)-net over F₉, using

4 times m-reduction [i] based on digital (79, 132, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 66, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(79, 79+49, 845)-Net over F₉ — Digital

Digital (79, 128, 845)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+49, 137328)-Net in Base 9 — Upper bound on s

There is no (79, 128, 137329)-net in base 9, because

1 times m-reduction [i] would yield (79, 127, 137329)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 447159 699928 893482 100792 901616 413787 531389 431861 263041 061163 125125 993392 926890 409984 318364 302441 887231 821594 071825 797569 > 9¹²⁷ [i]