MinT - Best Known (163−69, 163, s)-Nets in Base 8

Best Known (163−69, 163, s)-Nets in Base 8

(163−69, 163, 354)-Net over F₈ — Constructive and digital

Digital (94, 163, 354)-net over F₈, using

t-expansion [i] based on digital (93, 163, 354)-net over F₈, using
- 9 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]

(163−69, 163, 529)-Net over F₈ — Digital

Digital (94, 163, 529)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−69, 163, 38823)-Net in Base 8 — Upper bound on s

There is no (94, 163, 38824)-net in base 8, because

1 times m-reduction [i] would yield (94, 162, 38824)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 199 846904 213139 334656 281106 337669 809227 016540 238603 856106 415296 780470 045860 378829 295371 106549 870530 553778 036139 607093 730519 284910 002152 306889 244561 > 8¹⁶² [i]