MinT - Best Known (126, 126+36, s)-Nets in Base 3

Best Known (126, 126+36, s)-Nets in Base 3

(126, 126+36, 600)-Net over F₃ — Constructive and digital

Digital (126, 162, 600)-net over F₃, using

3² times duplication [i] based on digital (124, 160, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 40, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(126, 126+36, 1141)-Net over F₃ — Digital

Digital (126, 162, 1141)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+36, 74317)-Net in Base 3 — Upper bound on s

There is no (126, 162, 74318)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 196667 014697 274508 485998 233637 570007 631553 384960 607527 773680 217285 407650 932605 > 3¹⁶² [i]