MinT - Best Known (131, 131+59, s)-Nets in Base 3

Best Known (131, 131+59, s)-Nets in Base 3

(131, 131+59, 192)-Net over F₃ — Constructive and digital

Digital (131, 190, 192)-net over F₃, using

3¹ times duplication [i] based on digital (130, 189, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 63, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(131, 131+59, 380)-Net over F₃ — Digital

Digital (131, 190, 380)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+59, 7480)-Net in Base 3 — Upper bound on s

There is no (131, 190, 7481)-net in base 3, because

1 times m-reduction [i] would yield (131, 189, 7481)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 499598 578843 154425 070384 823902 791467 827589 339704 622789 665657 690079 222064 693912 459799 917571 > 3¹⁸⁹ [i]