MinT - Best Known (28, 143, s)-Nets in Base 9

Best Known (28, 143, s)-Nets in Base 9

(28, 143, 78)-Net over F₉ — Constructive and digital

Digital (28, 143, 78)-net over F₉, using

t-expansion [i] based on digital (22, 143, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(28, 143, 110)-Net over F₉ — Digital

Digital (28, 143, 110)-net over F₉, using

t-expansion [i] based on digital (26, 143, 110)-net over F₉, using
- net from sequence [i] based on digital (26, 109)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
    - a curve from the manYPoints database [i]

(28, 143, 623)-Net in Base 9 — Upper bound on s

There is no (28, 143, 624)-net in base 9, because

1 times m-reduction [i] would yield (28, 142, 624)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3384 152490 760227 004614 540209 187729 582994 085722 774854 158043 769374 487609 865160 140168 892562 792901 253096 834864 864250 222630 115037 745466 908545 > 9¹⁴² [i]