MinT - Best Known (93−31, 93, s)-Nets in Base 9

Best Known (93−31, 93, s)-Nets in Base 9

(93−31, 93, 448)-Net over F₉ — Constructive and digital

Digital (62, 93, 448)-net over F₉, using

5 times m-reduction [i] based on digital (62, 98, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 49, 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]

(93−31, 93, 1382)-Net over F₉ — Digital

Digital (62, 93, 1382)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−31, 93, 571949)-Net in Base 9 — Upper bound on s

There is no (62, 93, 571950)-net in base 9, because

1 times m-reduction [i] would yield (62, 92, 571950)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6170 526790 640591 985017 250659 011586 620060 139541 058068 660808 728803 499936 991635 362972 138961 > 9⁹² [i]