MinT - Best Known (73−26, 73, s)-Nets in Base 8

Best Known (73−26, 73, s)-Nets in Base 8

(73−26, 73, 354)-Net over F₈ — Constructive and digital

Digital (47, 73, 354)-net over F₈, using

7 times m-reduction [i] based on digital (47, 80, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 40, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(73−26, 73, 516)-Net in Base 8 — Constructive

(47, 73, 516)-net in base 8, using

8¹ times duplication [i] based on (46, 72, 516)-net in base 8, using
- base change [i] based on digital (28, 54, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 27, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(73−26, 73, 643)-Net over F₈ — Digital

Digital (47, 73, 643)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(73−26, 73, 95382)-Net in Base 8 — Upper bound on s

There is no (47, 73, 95383)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 842523 371711 072347 592695 393742 630524 581134 578018 194901 306144 089316 > 8⁷³ [i]