MinT - Best Known (42, 42+32, s)-Nets in Base 9

Best Known (42, 42+32, s)-Nets in Base 9

(42, 42+32, 320)-Net over F₉ — Constructive and digital

Digital (42, 74, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 37, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(42, 42+32, 334)-Net over F₉ — Digital

Digital (42, 74, 334)-net over F₉, using

trace code for nets [i] based on digital (5, 37, 167)-net over F₈₁, using
- net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
    - a curve from the manYPoints database [i]

(42, 42+32, 22010)-Net in Base 9 — Upper bound on s

There is no (42, 74, 22011)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 41120 143188 165230 047561 699551 359058 826918 988324 079964 420883 121159 219585 > 9⁷⁴ [i]