MinT - Best Known (132−53, 132, s)-Nets in Base 8

Best Known (132−53, 132, s)-Nets in Base 8

(132−53, 132, 354)-Net over F₈ — Constructive and digital

Digital (79, 132, 354)-net over F₈, using

12 times m-reduction [i] based on digital (79, 144, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 72, 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]

(132−53, 132, 384)-Net in Base 8 — Constructive

(79, 132, 384)-net in base 8, using

trace code for nets [i] based on (13, 66, 192)-net in base 64, using
- 4 times m-reduction [i] based on (13, 70, 192)-net in base 64, using
  - base change [i] based on digital (3, 60, 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]

(132−53, 132, 565)-Net over F₈ — Digital

Digital (79, 132, 565)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−53, 132, 53486)-Net in Base 8 — Upper bound on s

There is no (79, 132, 53487)-net in base 8, because

1 times m-reduction [i] would yield (79, 131, 53487)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 20174 668598 528142 716353 605178 819881 488610 162790 898686 020858 364071 662522 776016 479498 463506 719494 712553 096708 166791 599910 > 8¹³¹ [i]