MinT - Best Known (137−37, 137, s)-Nets in Base 3

Best Known (137−37, 137, s)-Nets in Base 3

(137−37, 137, 252)-Net over F₃ — Constructive and digital

Digital (100, 137, 252)-net over F₃, using

1 times m-reduction [i] based on digital (100, 138, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 46, 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]

(137−37, 137, 468)-Net over F₃ — Digital

Digital (100, 137, 468)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−37, 137, 15188)-Net in Base 3 — Upper bound on s

There is no (100, 137, 15189)-net in base 3, because

1 times m-reduction [i] would yield (100, 136, 15189)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 77396 507417 202165 740723 678614 096495 109281 310945 338192 222297 110705 > 3¹³⁶ [i]