MinT - Best Known (72, 72+63, s)-Nets in Base 9

Best Known (72, 72+63, s)-Nets in Base 9

(72, 72+63, 300)-Net over F₉ — Constructive and digital

Digital (72, 135, 300)-net over F₉, using

1 times m-reduction [i] based on digital (72, 136, 300)-net over F₉, using
- trace code for nets [i] based on digital (4, 68, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(72, 72+63, 341)-Net over F₉ — Digital

Digital (72, 135, 341)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+63, 20669)-Net in Base 9 — Upper bound on s

There is no (72, 135, 20670)-net in base 9, because

1 times m-reduction [i] would yield (72, 134, 20670)-net in base 9, but
- 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]