MinT - Best Known (156−69, 156, s)-Nets in Base 8

Best Known (156−69, 156, s)-Nets in Base 8

(156−69, 156, 354)-Net over F₈ — Constructive and digital

Digital (87, 156, 354)-net over F₈, using

4 times m-reduction [i] based on digital (87, 160, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 80, 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]

(156−69, 156, 421)-Net over F₈ — Digital

Digital (87, 156, 421)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−69, 156, 25295)-Net in Base 8 — Upper bound on s

There is no (87, 156, 25296)-net in base 8, because

1 times m-reduction [i] would yield (87, 155, 25296)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 95 365228 524519 840473 847214 603107 843550 816631 754278 538898 749816 111221 637127 473213 136726 899519 425913 862315 907497 258831 880892 319340 021077 040170 > 8¹⁵⁵ [i]