MinT - Best Known (166−137, 166, s)-Nets in Base 8

Best Known (166−137, 166, s)-Nets in Base 8

(166−137, 166, 65)-Net over F₈ — Constructive and digital

Digital (29, 166, 65)-net over F₈, using

t-expansion [i] based on digital (14, 166, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(166−137, 166, 97)-Net over F₈ — Digital

Digital (29, 166, 97)-net over F₈, using

t-expansion [i] based on digital (28, 166, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(166−137, 166, 538)-Net in Base 8 — Upper bound on s

There is no (29, 166, 539)-net in base 8, because

1 times m-reduction [i] would yield (29, 165, 539)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 112207 286475 445132 560051 302089 153603 211945 255622 062334 484449 724358 253112 467933 097022 806701 108787 211524 588834 301526 330932 807919 824892 446301 077153 821840 > 8¹⁶⁵ [i]