MinT - Best Known (28, 28+105, s)-Nets in Base 9

Best Known (28, 28+105, s)-Nets in Base 9

(28, 28+105, 78)-Net over F₉ — Constructive and digital

Digital (28, 133, 78)-net over F₉, using

t-expansion [i] based on digital (22, 133, 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, 28+105, 110)-Net over F₉ — Digital

Digital (28, 133, 110)-net over F₉, using

t-expansion [i] based on digital (26, 133, 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, 28+105, 636)-Net in Base 9 — Upper bound on s

There is no (28, 133, 637)-net in base 9, because

1 times m-reduction [i] would yield (28, 132, 637)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 914879 365187 899214 525463 397901 300372 662582 238961 594363 614932 363186 297099 214925 705393 524457 731967 036988 332564 784744 063419 245985 > 9¹³² [i]