MinT - Best Known (82−25, 82, s)-Nets in Base 9

Best Known (82−25, 82, s)-Nets in Base 9

(82−25, 82, 740)-Net over F₉ — Constructive and digital

Digital (57, 82, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 41, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(82−25, 82, 2243)-Net over F₉ — Digital

Digital (57, 82, 2243)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(82−25, 82, 1825604)-Net in Base 9 — Upper bound on s

There is no (57, 82, 1825605)-net in base 9, because

1 times m-reduction [i] would yield (57, 81, 1825605)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 196627 682672 782577 180038 494792 385828 018620 873876 108666 279526 025916 649911 216481 > 9⁸¹ [i]