MinT - Best Known (58, 89, s)-Nets in Base 9

Best Known (58, 89, s)-Nets in Base 9

(58, 89, 448)-Net over F₉ — Constructive and digital

Digital (58, 89, 448)-net over F₉, using

1 times m-reduction [i] based on digital (58, 90, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 45, 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]

(58, 89, 1035)-Net over F₉ — Digital

Digital (58, 89, 1035)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 89, 318337)-Net in Base 9 — Upper bound on s

There is no (58, 89, 318338)-net in base 9, because

1 times m-reduction [i] would yield (58, 88, 318338)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 940500 558550 029378 681128 694161 903767 807681 442945 070671 045429 299960 520832 849569 557425 > 9⁸⁸ [i]