MinT - Best Known (131, 131+52, s)-Nets in Base 3

Best Known (131, 131+52, s)-Nets in Base 3

(131, 131+52, 264)-Net over F₃ — Constructive and digital

Digital (131, 183, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 61, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(131, 131+52, 492)-Net over F₃ — Digital

Digital (131, 183, 492)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+52, 12009)-Net in Base 3 — Upper bound on s

There is no (131, 183, 12010)-net in base 3, because

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]