MinT - Best Known (108−44, 108, s)-Nets in Base 8

Best Known (108−44, 108, s)-Nets in Base 8

(108−44, 108, 354)-Net over F₈ — Constructive and digital

Digital (64, 108, 354)-net over F₈, using

6 times m-reduction [i] based on digital (64, 114, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 57, 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]

(108−44, 108, 450)-Net over F₈ — Digital

Digital (64, 108, 450)-net over F₈, using

trace code for nets [i] based on digital (10, 54, 225)-net over F₆₄, using
- net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(108−44, 108, 35070)-Net in Base 8 — Upper bound on s

There is no (64, 108, 35071)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 34 195200 857263 072478 491910 832423 678947 013533 631663 578486 124366 652723 648993 107897 648402 626481 882839 > 8¹⁰⁸ [i]