MinT - Best Known (135−106, 135, s)-Nets in Base 9

Best Known (135−106, 135, s)-Nets in Base 9

(135−106, 135, 78)-Net over F₉ — Constructive and digital

Digital (29, 135, 78)-net over F₉, using

t-expansion [i] based on digital (22, 135, 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]

(135−106, 135, 110)-Net over F₉ — Digital

Digital (29, 135, 110)-net over F₉, using

t-expansion [i] based on digital (26, 135, 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]

(135−106, 135, 661)-Net in Base 9 — Upper bound on s

There is no (29, 135, 662)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 677 717815 724812 773253 153346 674849 404559 309523 966931 058173 757642 448795 289447 043086 647752 271310 121487 472090 610809 388616 437665 242865 > 9¹³⁵ [i]