MinT - Best Known (127−44, 127, s)-Nets in Base 3

Best Known (127−44, 127, s)-Nets in Base 3

(127−44, 127, 148)-Net over F₃ — Constructive and digital

Digital (83, 127, 148)-net over F₃, using

5 times m-reduction [i] based on digital (83, 132, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 66, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(127−44, 127, 195)-Net over F₃ — Digital

Digital (83, 127, 195)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(127−44, 127, 2549)-Net in Base 3 — Upper bound on s

There is no (83, 127, 2550)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 942019 908169 375758 621376 759260 597621 795945 294693 003537 260181 > 3¹²⁷ [i]