MinT - Best Known (131, 131+53, s)-Nets in Base 3

Best Known (131, 131+53, s)-Nets in Base 3

(131, 131+53, 252)-Net over F₃ — Constructive and digital

Digital (131, 184, 252)-net over F₃, using

3¹ times duplication [i] based on digital (130, 183, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 61, 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]

(131, 131+53, 472)-Net over F₃ — Digital

Digital (131, 184, 472)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+53, 12009)-Net in Base 3 — Upper bound on s

There is no (131, 184, 12010)-net in base 3, because

1 times m-reduction [i] would yield (131, 183, 12010)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2056 871970 001014 515463 916091 835786 268999 608494 668378 819642 475913 200883 599811 153440 984373 > 3¹⁸³ [i]