MinT - Best Known (68, 68+82, s)-Nets in Base 9

Best Known (68, 68+82, s)-Nets in Base 9

(68, 68+82, 165)-Net over F₉ — Constructive and digital

Digital (68, 150, 165)-net over F₉, using

t-expansion [i] based on digital (64, 150, 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]

(68, 68+82, 192)-Net over F₉ — Digital

Digital (68, 150, 192)-net over F₉, using

t-expansion [i] based on digital (61, 150, 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]

(68, 68+82, 6225)-Net in Base 9 — Upper bound on s

There is no (68, 150, 6226)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 136918 379895 517478 728090 103063 628591 210160 711138 960285 309930 333744 929879 698758 259081 157026 974089 782346 973565 637999 797976 349990 557615 771176 679441 > 9¹⁵⁰ [i]