MinT - Best Known (97−37, 97, s)-Nets in Base 8

Best Known (97−37, 97, s)-Nets in Base 8

(97−37, 97, 354)-Net over F₈ — Constructive and digital

Digital (60, 97, 354)-net over F₈, using

9 times m-reduction [i] based on digital (60, 106, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 53, 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]

(97−37, 97, 384)-Net in Base 8 — Constructive

(60, 97, 384)-net in base 8, using

t-expansion [i] based on (59, 97, 384)-net in base 8, using
- 1 times m-reduction [i] based on (59, 98, 384)-net in base 8, using
  - trace code for nets [i] based on (10, 49, 192)-net in base 64, using
    - base change [i] based on digital (3, 42, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(97−37, 97, 571)-Net over F₈ — Digital

Digital (60, 97, 571)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(97−37, 97, 70703)-Net in Base 8 — Upper bound on s

There is no (60, 97, 70704)-net in base 8, because

1 times m-reduction [i] would yield (60, 96, 70704)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 497 323932 242996 791214 415537 240919 876219 355491 366818 191724 436084 726750 446939 912854 117690 > 8⁹⁶ [i]