MinT - Best Known (83, 83+81, s)-Nets in Base 8

Best Known (83, 83+81, s)-Nets in Base 8

(83, 83+81, 160)-Net over F₈ — Constructive and digital

Digital (83, 164, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 82, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(83, 83+81, 225)-Net in Base 8 — Constructive

(83, 164, 225)-net in base 8, using

8 times m-reduction [i] based on (83, 172, 225)-net in base 8, using
- base change [i] based on digital (40, 129, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(83, 83+81, 277)-Net over F₈ — Digital

Digital (83, 164, 277)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+81, 10758)-Net in Base 8 — Upper bound on s

There is no (83, 164, 10759)-net in base 8, because

1 times m-reduction [i] would yield (83, 163, 10759)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1598 777180 596707 773555 890364 823038 632263 010099 214309 854361 208213 806852 452345 011959 383209 188446 004422 130031 672050 195439 004390 915756 827374 467660 611648 > 8¹⁶³ [i]