MinT - Best Known (147−81, 147, s)-Nets in Base 9

Best Known (147−81, 147, s)-Nets in Base 9

(147−81, 147, 165)-Net over F₉ — Constructive and digital

Digital (66, 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]

(147−81, 147, 192)-Net over F₉ — Digital

Digital (66, 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]

(147−81, 147, 5969)-Net in Base 9 — Upper bound on s

There is no (66, 147, 5970)-net in base 9, because

1 times m-reduction [i] would yield (66, 146, 5970)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 988813 863564 767576 210184 961218 810630 868936 143775 956787 549743 235580 235775 202416 651438 888566 359070 753336 197725 184109 156502 788931 929900 935041 > 9¹⁴⁶ [i]