MinT - Best Known (90, 90+60, s)-Nets in Base 9

Best Known (90, 90+60, s)-Nets in Base 9

(90, 90+60, 448)-Net over F₉ — Constructive and digital

Digital (90, 150, 448)-net over F₉, using

t-expansion [i] based on digital (88, 150, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 75, 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]

(90, 90+60, 763)-Net over F₉ — Digital

Digital (90, 150, 763)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+60, 88883)-Net in Base 9 — Upper bound on s

There is no (90, 150, 88884)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 136905 831832 591249 299803 937859 796671 895397 858600 733853 675617 719829 753254 178303 658514 299373 852012 328358 795074 116930 827095 769571 384064 961414 107713 > 9¹⁵⁰ [i]