MinT - Best Known (72−26, 72, s)-Nets in Base 3

Best Known (72−26, 72, s)-Nets in Base 3

(72−26, 72, 80)-Net over F₃ — Constructive and digital

Digital (46, 72, 80)-net over F₃, using

4 times m-reduction [i] based on digital (46, 76, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 38, 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]

(72−26, 72, 111)-Net over F₃ — Digital

Digital (46, 72, 111)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(72−26, 72, 1231)-Net in Base 3 — Upper bound on s

There is no (46, 72, 1232)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22584 256648 152996 142354 723675 973281 > 3⁷² [i]