MinT - Best Known (142−56, 142, s)-Nets in Base 8

Best Known (142−56, 142, s)-Nets in Base 8

(142−56, 142, 354)-Net over F₈ — Constructive and digital

Digital (86, 142, 354)-net over F₈, using

16 times m-reduction [i] based on digital (86, 158, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 79, 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]

(142−56, 142, 384)-Net in Base 8 — Constructive

(86, 142, 384)-net in base 8, using

2 times m-reduction [i] based on (86, 144, 384)-net in base 8, using
- trace code for nets [i] based on (14, 72, 192)-net in base 64, using
  - 5 times m-reduction [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]

(142−56, 142, 654)-Net over F₈ — Digital

Digital (86, 142, 654)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−56, 142, 61339)-Net in Base 8 — Upper bound on s

There is no (86, 142, 61340)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 339828 639627 283755 252314 462244 873744 601612 035603 224659 451010 860871 221341 471686 985887 462018 687175 509972 620715 236288 853529 411264 > 8¹⁴² [i]