MinT - Best Known (182−51, 182, s)-Nets in Base 3

Best Known (182−51, 182, s)-Nets in Base 3

(182−51, 182, 264)-Net over F₃ — Constructive and digital

Digital (131, 182, 264)-net over F₃, using

1 times m-reduction [i] based on 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]

(182−51, 182, 514)-Net over F₃ — Digital

Digital (131, 182, 514)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−51, 182, 14461)-Net in Base 3 — Upper bound on s

There is no (131, 182, 14462)-net in base 3, because

1 times m-reduction [i] would yield (131, 181, 14462)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 228 653581 307580 516109 756852 578257 620317 707150 804259 155522 736438 662861 080849 162449 663309 > 3¹⁸¹ [i]