MinT - Best Known (162−104, 162, s)-Nets in Base 8

Best Known (162−104, 162, s)-Nets in Base 8

(162−104, 162, 98)-Net over F₈ — Constructive and digital

Digital (58, 162, 98)-net over F₈, using

t-expansion [i] based on digital (37, 162, 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]

(162−104, 162, 144)-Net over F₈ — Digital

Digital (58, 162, 144)-net over F₈, using

t-expansion [i] based on digital (45, 162, 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]

(162−104, 162, 1847)-Net in Base 8 — Upper bound on s

There is no (58, 162, 1848)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 201 244422 750666 710696 845041 247489 388009 344720 600113 275220 443435 239563 451887 920884 949052 030886 837165 268889 991344 728424 302374 813014 319262 201693 039939 > 8¹⁶² [i]