MinT - Best Known (138−30, 138, s)-Nets in Base 3

Best Known (138−30, 138, s)-Nets in Base 3

(138−30, 138, 600)-Net over F₃ — Constructive and digital

Digital (108, 138, 600)-net over F₃, using

3² times duplication [i] based on digital (106, 136, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 34, 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]

(138−30, 138, 1102)-Net over F₃ — Digital

Digital (108, 138, 1102)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−30, 138, 78735)-Net in Base 3 — Upper bound on s

There is no (108, 138, 78736)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 696225 666331 440398 142860 864219 658309 005708 049327 243123 059858 267841 > 3¹³⁸ [i]