MinT - Best Known (148−52, 148, s)-Nets in Base 8

Best Known (148−52, 148, s)-Nets in Base 8

(148−52, 148, 379)-Net over F₈ — Constructive and digital

Digital (96, 148, 379)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (4, 30, 25)-net over F₈, using
  - net from sequence [i] based on digital (4, 24)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
      - a function field by SÃ©mirat [i]
2. 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]

(148−52, 148, 576)-Net in Base 8 — Constructive

(96, 148, 576)-net in base 8, using

4 times m-reduction [i] based on (96, 152, 576)-net in base 8, using
- trace code for nets [i] based on (20, 76, 288)-net in base 64, using
  - 1 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
    - base change [i] based on digital (9, 66, 288)-net over F₁₂₈, using
      - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(148−52, 148, 1210)-Net over F₈ — Digital

Digital (96, 148, 1210)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−52, 148, 208366)-Net in Base 8 — Upper bound on s

There is no (96, 148, 208367)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 431914 909884 002000 741197 583746 741553 879334 604499 627344 910161 877782 776912 500931 845294 861119 154879 579797 777666 782574 897616 663081 407670 > 8¹⁴⁸ [i]