MinT - Best Known (93, 93+71, s)-Nets in Base 8

Best Known (93, 93+71, s)-Nets in Base 8

(93, 93+71, 354)-Net over F₈ — Constructive and digital

Digital (93, 164, 354)-net over F₈, using

8 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]

(93, 93+71, 482)-Net over F₈ — Digital

Digital (93, 164, 482)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(93, 93+71, 31892)-Net in Base 8 — Upper bound on s

There is no (93, 164, 31893)-net in base 8, because

1 times m-reduction [i] would yield (93, 163, 31893)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1599 617876 081790 928169 756143 008772 296099 877564 177217 461095 000930 274332 403485 042343 434625 765923 641630 837314 242691 704116 061405 542373 435587 461016 763056 > 8¹⁶³ [i]