MinT - Best Known (62, 62+35, s)-Nets in Base 8

Best Known (62, 62+35, s)-Nets in Base 8

(62, 62+35, 354)-Net over F₈ — Constructive and digital

Digital (62, 97, 354)-net over F₈, using

13 times m-reduction [i] based on digital (62, 110, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 55, 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]

(62, 62+35, 516)-Net in Base 8 — Constructive

(62, 97, 516)-net in base 8, using

8¹ times duplication [i] based on (61, 96, 516)-net in base 8, using
- base change [i] based on digital (37, 72, 516)-net over F₁₆, using
  - trace code for nets [i] based on digital (1, 36, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(62, 62+35, 746)-Net over F₈ — Digital

Digital (62, 97, 746)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(62, 62+35, 129007)-Net in Base 8 — Upper bound on s

There is no (62, 97, 129008)-net in base 8, because

1 times m-reduction [i] would yield (62, 96, 129008)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 497 368028 565363 271643 871870 718943 289806 622155 031602 054106 318445 378755 894206 379877 032742 > 8⁹⁶ [i]