MinT - Best Known (165−118, 165, s)-Nets in Base 8

Best Known (165−118, 165, s)-Nets in Base 8

(165−118, 165, 98)-Net over F₈ — Constructive and digital

Digital (47, 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]

(165−118, 165, 144)-Net over F₈ — Digital

Digital (47, 165, 144)-net over F₈, using

t-expansion [i] based on digital (45, 165, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(165−118, 165, 1056)-Net in Base 8 — Upper bound on s

There is no (47, 165, 1057)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 105163 638348 551066 283528 115887 173885 460463 453080 637015 990171 174272 764093 782552 651050 076751 618881 862179 062548 875161 893739 388450 427580 818578 238101 171200 > 8¹⁶⁵ [i]