MinT - Best Known (118−52, 118, s)-Nets in Base 8

Best Known (118−52, 118, s)-Nets in Base 8

(118−52, 118, 354)-Net over F₈ — Constructive and digital

Digital (66, 118, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 59, 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]

(118−52, 118, 18900)-Net in Base 8 — Upper bound on s

There is no (66, 118, 18901)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 36746 351101 167735 100891 982170 400037 051029 404082 270387 080612 575100 077299 190217 709808 182848 153027 766298 224080 > 8¹¹⁸ [i]