MinT - Best Known (147−51, 147, s)-Nets in Base 8

Best Known (147−51, 147, s)-Nets in Base 8

(147−51, 147, 382)-Net over F₈ — Constructive and digital

Digital (96, 147, 382)-net over F₈, using

8¹ times duplication [i] based on digital (95, 146, 382)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (5, 30, 28)-net over F₈, using
    - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
        a function field by SÃ©mirat [i]
  2. digital (65, 116, 354)-net over F₈, using
    - trace code for nets [i] based on digital (7, 58, 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]

(147−51, 147, 576)-Net in Base 8 — Constructive

(96, 147, 576)-net in base 8, using

5 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]

(147−51, 147, 1283)-Net over F₈ — Digital

Digital (96, 147, 1283)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−51, 147, 273242)-Net in Base 8 — Upper bound on s

There is no (96, 147, 273243)-net in base 8, because

1 times m-reduction [i] would yield (96, 146, 273243)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 709823 133993 614263 693066 024794 574260 801465 126007 004865 614675 865591 050342 713382 047355 361428 513570 084894 525432 201062 816223 866628 287126 > 8¹⁴⁶ [i]