MinT - Best Known (138−38, 138, s)-Nets in Base 3

Best Known (138−38, 138, s)-Nets in Base 3

(138−38, 138, 252)-Net over F₃ — Constructive and digital

Digital (100, 138, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 46, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(138−38, 138, 438)-Net over F₃ — Digital

Digital (100, 138, 438)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−38, 138, 11558)-Net in Base 3 — Upper bound on s

There is no (100, 138, 11559)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 696863 132956 988757 982008 475490 148959 385039 550322 849002 215755 362683 > 3¹³⁸ [i]