MinT - Best Known (101, 101+57, s)-Nets in Base 3

Best Known (101, 101+57, s)-Nets in Base 3

(101, 101+57, 156)-Net over F₃ — Constructive and digital

Digital (101, 158, 156)-net over F₃, using

trace code for nets [i] based on digital (22, 79, 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]

(101, 101+57, 205)-Net over F₃ — Digital

Digital (101, 158, 205)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+57, 2647)-Net in Base 3 — Upper bound on s

There is no (101, 158, 2648)-net in base 3, because

1 times m-reduction [i] would yield (101, 157, 2648)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 815 649995 971836 204103 713476 857365 344456 690660 411028 540629 584550 780878 451393 > 3¹⁵⁷ [i]