MinT - Best Known (145−115, 145, s)-Nets in Base 9

Best Known (145−115, 145, s)-Nets in Base 9

(145−115, 145, 78)-Net over F₉ — Constructive and digital

Digital (30, 145, 78)-net over F₉, using

t-expansion [i] based on digital (22, 145, 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]

(145−115, 145, 110)-Net over F₉ — Digital

Digital (30, 145, 110)-net over F₉, using

t-expansion [i] based on digital (26, 145, 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]

(145−115, 145, 675)-Net in Base 9 — Upper bound on s

There is no (30, 145, 676)-net in base 9, because

1 times m-reduction [i] would yield (30, 144, 676)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 258234 645480 764549 312772 712165 624120 134647 359263 182783 919604 441519 658729 865212 266307 395457 318708 867999 297636 369010 693578 755091 125919 660577 > 9¹⁴⁴ [i]