MinT - Best Known (82, 121, s)-Nets in Base 9

Best Known (82, 121, s)-Nets in Base 9

(82, 121, 740)-Net over F₉ — Constructive and digital

Digital (82, 121, 740)-net over F₉, using

11 times m-reduction [i] based on digital (82, 132, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 66, 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]

(82, 121, 2071)-Net over F₉ — Digital

Digital (82, 121, 2071)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 121, 1054182)-Net in Base 9 — Upper bound on s

There is no (82, 121, 1054183)-net in base 9, because

1 times m-reduction [i] would yield (82, 120, 1054183)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3 229299 520270 531866 493816 606562 156449 971296 557259 876503 328185 975130 675696 133753 322371 421505 648424 180296 767700 050473 > 9¹²⁰ [i]