MinT - Best Known (162−67, 162, s)-Nets in Base 8

Best Known (162−67, 162, s)-Nets in Base 8

(162−67, 162, 354)-Net over F₈ — Constructive and digital

Digital (95, 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]

(162−67, 162, 584)-Net over F₈ — Digital

Digital (95, 162, 584)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−67, 162, 47868)-Net in Base 8 — Upper bound on s

There is no (95, 162, 47869)-net in base 8, because

1 times m-reduction [i] would yield (95, 161, 47869)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 24 977152 762744 749544 219823 092790 873526 571825 957114 202321 728296 015628 795915 009854 441282 839014 866812 293256 675172 689103 251739 258924 277481 732730 105580 > 8¹⁶¹ [i]