MinT - Best Known (121−92, 121, s)-Nets in Base 9

Best Known (121−92, 121, s)-Nets in Base 9

(121−92, 121, 78)-Net over F₉ — Constructive and digital

Digital (29, 121, 78)-net over F₉, using

t-expansion [i] based on digital (22, 121, 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]

(121−92, 121, 110)-Net over F₉ — Digital

Digital (29, 121, 110)-net over F₉, using

t-expansion [i] based on digital (26, 121, 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]

(121−92, 121, 700)-Net in Base 9 — Upper bound on s

There is no (29, 121, 701)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 30 565758 114030 805735 147421 736340 848500 696683 314400 066457 215852 404432 137318 270268 639311 246245 816902 891010 447990 945777 > 9¹²¹ [i]