MinT - Best Known (69, 69+29, s)-Nets in Base 9

Best Known (69, 69+29, s)-Nets in Base 9

(69, 69+29, 740)-Net over F₉ — Constructive and digital

Digital (69, 98, 740)-net over F₉, using

8 times m-reduction [i] based on digital (69, 106, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 53, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(69, 69+29, 3103)-Net over F₉ — Digital

Digital (69, 98, 3103)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+29, 3089612)-Net in Base 9 — Upper bound on s

There is no (69, 98, 3089613)-net in base 9, because

1 times m-reduction [i] would yield (69, 97, 3089613)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 364 355117 990510 734224 999268 735341 889905 106423 433319 837558 795575 958709 417576 945834 132009 955313 > 9⁹⁷ [i]