MinT - Best Known (38, 38+28, s)-Nets in Base 9

Best Known (38, 38+28, s)-Nets in Base 9

(38, 38+28, 320)-Net over F₉ — Constructive and digital

Digital (38, 66, 320)-net over F₉, using

trace code for nets [i] based on digital (5, 33, 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]

(38, 38+28, 334)-Net over F₉ — Digital

Digital (38, 66, 334)-net over F₉, using

trace code for nets [i] based on digital (5, 33, 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]

(38, 38+28, 23811)-Net in Base 9 — Upper bound on s

There is no (38, 66, 23812)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 955 211746 787722 519895 373247 761312 674587 161022 028781 227823 400257 > 9⁶⁶ [i]