MinT - Best Known (165−124, 165, s)-Nets in Base 8

Best Known (165−124, 165, s)-Nets in Base 8

(165−124, 165, 98)-Net over F₈ — Constructive and digital

Digital (41, 165, 98)-net over F₈, using

t-expansion [i] based on digital (37, 165, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(165−124, 165, 129)-Net over F₈ — Digital

Digital (41, 165, 129)-net over F₈, using

t-expansion [i] based on digital (38, 165, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(165−124, 165, 826)-Net in Base 8 — Upper bound on s

There is no (41, 165, 827)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 104441 842305 457122 239739 411089 360145 153184 723597 879923 619028 750057 822154 773561 735734 809137 943040 935323 108366 528769 038342 668275 782614 770173 642160 968768 > 8¹⁶⁵ [i]