MinT - Best Known (126, 126+40, s)-Nets in Base 3

Best Known (126, 126+40, s)-Nets in Base 3

(126, 126+40, 400)-Net over F₃ — Constructive and digital

Digital (126, 166, 400)-net over F₃, using

3² times duplication [i] based on digital (124, 164, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 41, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(126, 126+40, 846)-Net over F₃ — Digital

Digital (126, 166, 846)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+40, 37858)-Net in Base 3 — Upper bound on s

There is no (126, 166, 37859)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15 934182 351872 212287 212393 803850 384226 038965 515279 835282 516939 205212 337660 918457 > 3¹⁶⁶ [i]