MinT - Best Known (139−58, 139, s)-Nets in Base 3

Best Known (139−58, 139, s)-Nets in Base 3

(139−58, 139, 80)-Net over F₃ — Constructive and digital

Digital (81, 139, 80)-net over F₃, using

7 times m-reduction [i] based on digital (81, 146, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 73, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(139−58, 139, 122)-Net over F₃ — Digital

Digital (81, 139, 122)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−58, 139, 1101)-Net in Base 3 — Upper bound on s

There is no (81, 139, 1102)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 112891 494130 942160 100413 749159 180204 667995 011802 780559 788084 827397 > 3¹³⁹ [i]