MinT - Best Known (66, 66+38, s)-Nets in Base 8

Best Known (66, 66+38, s)-Nets in Base 8

(66, 66+38, 354)-Net over F₈ — Constructive and digital

Digital (66, 104, 354)-net over F₈, using

14 times m-reduction [i] based on digital (66, 118, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 59, 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]

(66, 66+38, 516)-Net in Base 8 — Constructive

(66, 104, 516)-net in base 8, using

base change [i] based on digital (40, 78, 516)-net over F₁₆, using
- trace code for nets [i] based on digital (1, 39, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(66, 66+38, 742)-Net over F₈ — Digital

Digital (66, 104, 742)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+38, 99379)-Net in Base 8 — Upper bound on s

There is no (66, 104, 99380)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8344 907892 897408 011075 669544 622820 218486 658345 384113 057396 123379 910049 854843 432234 630577 016577 > 8¹⁰⁴ [i]