MinT - Best Known (65, 65+84, s)-Nets in Base 9

Best Known (65, 65+84, s)-Nets in Base 9

(65, 65+84, 165)-Net over F₉ — Constructive and digital

Digital (65, 149, 165)-net over F₉, using

t-expansion [i] based on digital (64, 149, 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+84, 192)-Net over F₉ — Digital

Digital (65, 149, 192)-net over F₉, using

t-expansion [i] based on digital (61, 149, 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+84, 4986)-Net in Base 9 — Upper bound on s

There is no (65, 149, 4987)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15316 312893 259992 276622 843544 917349 437543 405878 369346 499888 259957 787797 304046 815392 438979 727371 225349 250245 575010 378216 026667 278722 890693 675505 > 9¹⁴⁹ [i]