MinT - Best Known (105−64, 105, s)-Nets in Base 8

Best Known (105−64, 105, s)-Nets in Base 8

(105−64, 105, 98)-Net over F₈ — Constructive and digital

Digital (41, 105, 98)-net over F₈, using

t-expansion [i] based on digital (37, 105, 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]

(105−64, 105, 129)-Net over F₈ — Digital

Digital (41, 105, 129)-net over F₈, using

t-expansion [i] based on digital (38, 105, 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]

(105−64, 105, 1658)-Net in Base 8 — Upper bound on s

There is no (41, 105, 1659)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 66768 667953 388535 360817 691835 108499 621346 962820 543978 654897 914189 712310 985688 248760 638041 897565 > 8¹⁰⁵ [i]