MinT - Best Known (101, 101+38, s)-Nets in Base 3

Best Known (101, 101+38, s)-Nets in Base 3

(101, 101+38, 252)-Net over F₃ — Constructive and digital

Digital (101, 139, 252)-net over F₃, using

3¹ times duplication [i] based on digital (100, 138, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 46, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(101, 101+38, 452)-Net over F₃ — Digital

Digital (101, 139, 452)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+38, 12247)-Net in Base 3 — Upper bound on s

There is no (101, 139, 12248)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 090066 225733 845605 713088 561842 533466 431688 835978 136223 950340 855009 > 3¹³⁹ [i]