MinT - Best Known (151−60, 151, s)-Nets in Base 8

Best Known (151−60, 151, s)-Nets in Base 8

(151−60, 151, 354)-Net over F₈ — Constructive and digital

Digital (91, 151, 354)-net over F₈, using

17 times m-reduction [i] based on digital (91, 168, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 84, 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]

(151−60, 151, 384)-Net in Base 8 — Constructive

(91, 151, 384)-net in base 8, using

3 times m-reduction [i] based on (91, 154, 384)-net in base 8, using
- trace code for nets [i] based on (14, 77, 192)-net in base 64, using
  - base change [i] based on digital (3, 66, 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]

(151−60, 151, 664)-Net over F₈ — Digital

Digital (91, 151, 664)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(151−60, 151, 60409)-Net in Base 8 — Upper bound on s

There is no (91, 151, 60410)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23259 306453 786933 116296 144842 963467 750117 612686 469266 601231 280711 184193 225048 951229 260895 322842 139427 458466 491400 187705 763947 695117 499920 > 8¹⁵¹ [i]