MinT - Best Known (36, 59, s)-Nets in Base 9

Best Known (36, 59, s)-Nets in Base 9

(36, 59, 320)-Net over F₉ — Constructive and digital

Digital (36, 59, 320)-net over F₉, using

3 times m-reduction [i] based on digital (36, 62, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 31, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(36, 59, 421)-Net over F₉ — Digital

Digital (36, 59, 421)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(36, 59, 65969)-Net in Base 9 — Upper bound on s

There is no (36, 59, 65970)-net in base 9, because

1 times m-reduction [i] would yield (36, 58, 65970)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 22 187433 830622 079670 887680 124398 841831 233386 328330 176625 > 9⁵⁸ [i]