MinT - Best Known (141−59, 141, s)-Nets in Base 9

Best Known (141−59, 141, s)-Nets in Base 9

(141−59, 141, 344)-Net over F₉ — Constructive and digital

Digital (82, 141, 344)-net over F₉, using

9 times m-reduction [i] based on digital (82, 150, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 75, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(141−59, 141, 580)-Net over F₉ — Digital

Digital (82, 141, 580)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(141−59, 141, 58964)-Net in Base 9 — Upper bound on s

There is no (82, 141, 58965)-net in base 9, because

1 times m-reduction [i] would yield (82, 140, 58965)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 270757 207585 213522 799147 711777 521540 363047 461009 731815 265912 825220 172972 998224 552638 508375 165111 302826 071459 198698 935379 519316 313993 > 9¹⁴⁰ [i]