MinT - Best Known (106−84, 106, s)-Nets in Base 9

Best Known (106−84, 106, s)-Nets in Base 9

(106−84, 106, 78)-Net over F₉ — Constructive and digital

Digital (22, 106, 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]

(106−84, 106, 88)-Net over F₉ — Digital

Digital (22, 106, 88)-net over F₉, using

t-expansion [i] based on digital (21, 106, 88)-net over F₉, using
- net from sequence [i] based on digital (21, 87)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 21 and N(F) ≥ 88, using
    - a curve from the manYPoints database [i]

(106−84, 106, 503)-Net in Base 9 — Upper bound on s

There is no (22, 106, 504)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 151587 159159 998801 414034 686561 601413 090427 925546 969590 288098 575290 107386 336274 573160 727766 116450 738305 > 9¹⁰⁶ [i]