MinT - Best Known (41, 112, s)-Nets in Base 8

Best Known (41, 112, s)-Nets in Base 8

(41, 112, 98)-Net over F₈ — Constructive and digital

Digital (41, 112, 98)-net over F₈, using

t-expansion [i] based on digital (37, 112, 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]

(41, 112, 129)-Net over F₈ — Digital

Digital (41, 112, 129)-net over F₈, using

t-expansion [i] based on digital (38, 112, 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]

(41, 112, 1431)-Net in Base 8 — Upper bound on s

There is no (41, 112, 1432)-net in base 8, because

1 times m-reduction [i] would yield (41, 111, 1432)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 17901 706815 083187 200367 221135 442814 551415 020626 084899 677159 968420 419857 035867 602792 009445 381901 962572 > 8¹¹¹ [i]