MinT - Best Known (59, 59+27, s)-Nets in Base 9

Best Known (59, 59+27, s)-Nets in Base 9

(59, 59+27, 740)-Net over F₉ — Constructive and digital

Digital (59, 86, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 43, 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]

(59, 59+27, 1903)-Net over F₉ — Digital

Digital (59, 86, 1903)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+27, 1229111)-Net in Base 9 — Upper bound on s

There is no (59, 86, 1229112)-net in base 9, because

1 times m-reduction [i] would yield (59, 85, 1229112)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1290 070674 884534 495540 269208 802898 235732 008471 135381 918845 618442 548594 437455 139009 > 9⁸⁵ [i]