MinT - Best Known (77−40, 77, s)-Nets in Base 8

Best Known (77−40, 77, s)-Nets in Base 8

(77−40, 77, 98)-Net over F₈ — Constructive and digital

Digital (37, 77, 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]

(77−40, 77, 122)-Net over F₈ — Digital

Digital (37, 77, 122)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(77−40, 77, 3544)-Net in Base 8 — Upper bound on s

There is no (37, 77, 3545)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3454 243102 302242 915046 022742 138774 967992 001641 372876 321732 459849 137658 > 8⁷⁷ [i]