MinT - Best Known (147−119, 147, s)-Nets in Base 9

Best Known (147−119, 147, s)-Nets in Base 9

(147−119, 147, 78)-Net over F₉ — Constructive and digital

Digital (28, 147, 78)-net over F₉, using

t-expansion [i] based on digital (22, 147, 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]

(147−119, 147, 110)-Net over F₉ — Digital

Digital (28, 147, 110)-net over F₉, using

t-expansion [i] based on digital (26, 147, 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]

(147−119, 147, 619)-Net in Base 9 — Upper bound on s

There is no (28, 147, 620)-net in base 9, because

1 times m-reduction [i] would yield (28, 146, 620)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21 369077 509384 271382 373714 102744 361016 493449 549496 364769 045116 493482 378562 297201 196749 414910 123890 512903 394605 618936 761610 866890 997582 051233 > 9¹⁴⁶ [i]