MinT - Best Known (74, 74+65, s)-Nets in Base 9

Best Known (74, 74+65, s)-Nets in Base 9

(74, 74+65, 300)-Net over F₉ — Constructive and digital

Digital (74, 139, 300)-net over F₉, using

1 times m-reduction [i] based on digital (74, 140, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 70, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(74, 74+65, 346)-Net over F₉ — Digital

Digital (74, 139, 346)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+65, 20823)-Net in Base 9 — Upper bound on s

There is no (74, 139, 20824)-net in base 9, because

1 times m-reduction [i] would yield (74, 138, 20824)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 485025 906084 862987 812159 498192 424609 879879 467310 769495 368150 176142 428669 168074 015813 294721 448813 151784 692863 762650 053777 738387 892225 > 9¹³⁸ [i]