MinT - Best Known (134−62, 134, s)-Nets in Base 9

Best Known (134−62, 134, s)-Nets in Base 9

(134−62, 134, 320)-Net over F₉ — Constructive and digital

Digital (72, 134, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 67, 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]

(134−62, 134, 351)-Net over F₉ — Digital

Digital (72, 134, 351)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−62, 134, 20669)-Net in Base 9 — Upper bound on s

There is no (72, 134, 20670)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 73 893741 940251 031635 393756 330615 159478 553620 174425 320407 750003 141884 901970 868810 668859 736607 798289 062240 809688 633331 303081 600081 > 9¹³⁴ [i]