MinT - Best Known (61, 61+42, s)-Nets in Base 3

Best Known (61, 61+42, s)-Nets in Base 3

(61, 61+42, 80)-Net over F₃ — Constructive and digital

Digital (61, 103, 80)-net over F₃, using

3 times m-reduction [i] based on digital (61, 106, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 53, 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]

(61, 61+42, 102)-Net over F₃ — Digital

Digital (61, 103, 102)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+42, 929)-Net in Base 3 — Upper bound on s

There is no (61, 103, 930)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 14 077508 513882 508715 467824 232742 709522 386710 446781 > 3¹⁰³ [i]