MinT - Best Known (90−47, 90, s)-Nets in Base 8

Best Known (90−47, 90, s)-Nets in Base 8

(90−47, 90, 98)-Net over F₈ — Constructive and digital

Digital (43, 90, 98)-net over F₈, using

t-expansion [i] based on digital (37, 90, 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]

(90−47, 90, 134)-Net over F₈ — Digital

Digital (43, 90, 134)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−47, 90, 4192)-Net in Base 8 — Upper bound on s

There is no (43, 90, 4193)-net in base 8, because

1 times m-reduction [i] would yield (43, 89, 4193)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 238 106334 297883 307323 667736 468567 206975 672936 916048 163126 166608 889606 205862 169888 > 8⁸⁹ [i]