MinT - Best Known (101, 101+40, s)-Nets in Base 3

Best Known (101, 101+40, s)-Nets in Base 3

(101, 101+40, 246)-Net over F₃ — Constructive and digital

Digital (101, 141, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 47, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(101, 101+40, 400)-Net over F₃ — Digital

Digital (101, 141, 400)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+40, 9574)-Net in Base 3 — Upper bound on s

There is no (101, 141, 9575)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 832468 190773 130709 244677 760037 965152 909037 255029 121102 508348 184921 > 3¹⁴¹ [i]