MinT - Best Known (135−40, 135, s)-Nets in Base 3

Best Known (135−40, 135, s)-Nets in Base 3

(135−40, 135, 204)-Net over F₃ — Constructive and digital

Digital (95, 135, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 45, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(135−40, 135, 332)-Net over F₃ — Digital

Digital (95, 135, 332)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−40, 135, 6880)-Net in Base 3 — Upper bound on s

There is no (95, 135, 6881)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25826 022156 640019 762440 678280 833661 844008 083477 927023 551416 228497 > 3¹³⁵ [i]