MinT - Best Known (88, 88+61, s)-Nets in Base 9

Best Known (88, 88+61, s)-Nets in Base 9

(88, 88+61, 448)-Net over F₉ — Constructive and digital

Digital (88, 149, 448)-net over F₉, using

1 times m-reduction [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]

(88, 88+61, 676)-Net over F₉ — Digital

Digital (88, 149, 676)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+61, 76770)-Net in Base 9 — Upper bound on s

There is no (88, 149, 76771)-net in base 9, because

1 times m-reduction [i] would yield (88, 148, 76771)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1690 643708 566896 694700 400391 103627 231101 059124 752828 718314 239495 427519 180810 997418 885311 916527 668210 877365 029942 571957 923544 465529 922714 565969 > 9¹⁴⁸ [i]