MinT - Best Known (125, 125+121, s)-Nets in Base 3

Best Known (125, 125+121, s)-Nets in Base 3

(125, 125+121, 78)-Net over F₃ — Constructive and digital

Digital (125, 246, 78)-net over F₃, using

t-expansion [i] based on digital (121, 246, 78)-net over F₃, using
- net from sequence [i] based on digital (121, 77)-sequence over F₃, using
  - base reduction for sequences [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]

(125, 125+121, 126)-Net over F₃ — Digital

Digital (125, 246, 126)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(125, 125+121, 971)-Net in Base 3 — Upper bound on s

There is no (125, 246, 972)-net in base 3, because

1 times m-reduction [i] would yield (125, 245, 972)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 821 634562 564344 959084 977139 292185 668308 491927 791180 416680 102482 656303 764622 735200 260014 412400 532493 384966 504652 997697 > 3²⁴⁵ [i]