MinT - Best Known (161−105, 161, s)-Nets in Base 8

Best Known (161−105, 161, s)-Nets in Base 8

(161−105, 161, 98)-Net over F₈ — Constructive and digital

Digital (56, 161, 98)-net over F₈, using

t-expansion [i] based on digital (37, 161, 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]

(161−105, 161, 144)-Net over F₈ — Digital

Digital (56, 161, 144)-net over F₈, using

t-expansion [i] based on digital (45, 161, 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]

(161−105, 161, 1703)-Net in Base 8 — Upper bound on s

There is no (56, 161, 1704)-net in base 8, because

1 times m-reduction [i] would yield (56, 160, 1704)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 196444 885622 264375 591460 639033 267563 439552 337736 400038 325515 525845 336864 733351 479258 842173 949789 624817 272976 791547 573781 713757 959250 063513 696504 > 8¹⁶⁰ [i]