MinT - Best Known (135−38, 135, s)-Nets in Base 3

Best Known (135−38, 135, s)-Nets in Base 3

(135−38, 135, 246)-Net over F₃ — Constructive and digital

Digital (97, 135, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 45, 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]

(135−38, 135, 397)-Net over F₃ — Digital

Digital (97, 135, 397)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(135−38, 135, 9714)-Net in Base 3 — Upper bound on s

There is no (97, 135, 9715)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25797 312457 450553 883576 075970 014272 784646 685150 262515 900011 624011 > 3¹³⁵ [i]