MinT - Best Known (98−49, 98, s)-Nets in Base 9

Best Known (98−49, 98, s)-Nets in Base 9

(98−49, 98, 164)-Net over F₉ — Constructive and digital

Digital (49, 98, 164)-net over F₉, using

trace code for nets [i] based on digital (0, 49, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(98−49, 98, 195)-Net over F₉ — Digital

Digital (49, 98, 195)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(98−49, 98, 8796)-Net in Base 9 — Upper bound on s

There is no (49, 98, 8797)-net in base 9, because

1 times m-reduction [i] would yield (49, 97, 8797)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 365 293454 050374 722328 457670 461483 570411 813023 789982 250600 238793 454411 878914 825666 364046 775489 > 9⁹⁷ [i]