MinT - Best Known (65, 65+82, s)-Nets in Base 9

Best Known (65, 65+82, s)-Nets in Base 9

(65, 65+82, 165)-Net over F₉ — Constructive and digital

Digital (65, 147, 165)-net over F₉, using

t-expansion [i] based on digital (64, 147, 165)-net over F₉, using
- net from sequence [i] based on digital (64, 164)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 64 and N(F) ≥ 165, using
    - T₄ from the second tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(65, 65+82, 192)-Net over F₉ — Digital

Digital (65, 147, 192)-net over F₉, using

t-expansion [i] based on digital (61, 147, 192)-net over F₉, using
- net from sequence [i] based on digital (61, 191)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 61 and N(F) ≥ 192, using
    - Drinfeld modules of rank 1 [i]

(65, 65+82, 5297)-Net in Base 9 — Upper bound on s

There is no (65, 147, 5298)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 188 355175 993570 858002 912001 501042 177720 437569 194742 014246 059458 095855 031455 135621 431312 992594 781470 312317 880648 403811 569037 917367 876965 745425 > 9¹⁴⁷ [i]