MinT - Best Known (145−65, 145, s)-Nets in Base 3

Best Known (145−65, 145, s)-Nets in Base 3

(145−65, 145, 72)-Net over F₃ — Constructive and digital

Digital (80, 145, 72)-net over F₃, using

1 times m-reduction [i] based on digital (80, 146, 72)-net over F₃, using
- trace code for nets [i] based on digital (7, 73, 36)-net over F₉, using
  - net from sequence [i] based on digital (7, 35)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
      - a function field by SÃ©mirat [i]

(145−65, 145, 104)-Net over F₃ — Digital

Digital (80, 145, 104)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−65, 145, 866)-Net in Base 3 — Upper bound on s

There is no (80, 145, 867)-net in base 3, because

1 times m-reduction [i] would yield (80, 144, 867)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 522 831492 575980 653557 447435 709380 824113 777075 254461 478930 087135 749569 > 3¹⁴⁴ [i]