MinT - Best Known (162−64, 162, s)-Nets in Base 8

Best Known (162−64, 162, s)-Nets in Base 8

(162−64, 162, 354)-Net over F₈ — Constructive and digital

Digital (98, 162, 354)-net over F₈, using

t-expansion [i] based on digital (93, 162, 354)-net over F₈, using
- 10 times m-reduction [i] based on digital (93, 172, 354)-net over F₈, using
  - trace code for nets [i] based on digital (7, 86, 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]

(162−64, 162, 432)-Net in Base 8 — Constructive

(98, 162, 432)-net in base 8, using

trace code for nets [i] based on (17, 81, 216)-net in base 64, using
- 3 times m-reduction [i] based on (17, 84, 216)-net in base 64, using
  - base change [i] based on digital (5, 72, 216)-net over F₁₂₈, using
    - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(162−64, 162, 724)-Net over F₈ — Digital

Digital (98, 162, 724)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−64, 162, 68162)-Net in Base 8 — Upper bound on s

There is no (98, 162, 68163)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 199 809030 668104 419988 932775 553641 897869 249185 030353 348545 575915 652289 911155 279473 089499 135249 602588 698415 401724 054030 775550 101875 732007 793114 711190 > 8¹⁶² [i]