MinT - Best Known (110−39, 110, s)-Nets in Base 9

Best Known (110−39, 110, s)-Nets in Base 9

(110−39, 110, 740)-Net over F₉ — Constructive and digital

Digital (71, 110, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 55, 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]

(110−39, 110, 1105)-Net over F₉ — Digital

Digital (71, 110, 1105)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(110−39, 110, 295425)-Net in Base 9 — Upper bound on s

There is no (71, 110, 295426)-net in base 9, because

1 times m-reduction [i] would yield (71, 109, 295426)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 102 910197 096124 817892 554882 096590 587470 990302 464483 285186 606677 673561 952753 219918 005862 515983 041760 655729 > 9¹⁰⁹ [i]