MinT - Best Known (132−61, 132, s)-Nets in Base 9

Best Known (132−61, 132, s)-Nets in Base 9

(132−61, 132, 320)-Net over F₉ — Constructive and digital

Digital (71, 132, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 66, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(132−61, 132, 348)-Net over F₉ — Digital

Digital (71, 132, 348)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−61, 132, 22090)-Net in Base 9 — Upper bound on s

There is no (71, 132, 22091)-net in base 9, because

1 times m-reduction [i] would yield (71, 131, 22091)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101451 207773 102907 354190 922327 471183 448952 113055 025914 750436 876045 243224 661099 417782 010866 376118 723508 376084 217300 023492 294609 > 9¹³¹ [i]