MinT - Best Known (131−34, 131, s)-Nets in Base 3

Best Known (131−34, 131, s)-Nets in Base 3

(131−34, 131, 264)-Net over F₃ — Constructive and digital

Digital (97, 131, 264)-net over F₃, using

1 times m-reduction [i] based on digital (97, 132, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 44, 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]

(131−34, 131, 528)-Net over F₃ — Digital

Digital (97, 131, 528)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−34, 131, 17026)-Net in Base 3 — Upper bound on s

There is no (97, 131, 17027)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 318 374194 588118 042795 885860 383968 939816 484979 715830 433707 146087 > 3¹³¹ [i]