MinT - Best Known (115−86, 115, s)-Nets in Base 9

Best Known (115−86, 115, s)-Nets in Base 9

(115−86, 115, 78)-Net over F₉ — Constructive and digital

Digital (29, 115, 78)-net over F₉, using

t-expansion [i] based on digital (22, 115, 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]

(115−86, 115, 110)-Net over F₉ — Digital

Digital (29, 115, 110)-net over F₉, using

t-expansion [i] based on digital (26, 115, 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]

(115−86, 115, 726)-Net in Base 9 — Upper bound on s

There is no (29, 115, 727)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 57 092800 537162 384462 459162 116673 883855 111523 897024 804421 379655 848360 887319 422761 666774 306162 373955 569441 448937 > 9¹¹⁵ [i]