MinT - Best Known (75, 75+57, s)-Nets in Base 3

Best Known (75, 75+57, s)-Nets in Base 3

(75, 75+57, 80)-Net over F₃ — Constructive and digital

Digital (75, 132, 80)-net over F₃, using

2 times m-reduction [i] based on digital (75, 134, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 67, 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]

(75, 75+57, 106)-Net over F₃ — Digital

Digital (75, 132, 106)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+57, 937)-Net in Base 3 — Upper bound on s

There is no (75, 132, 938)-net in base 3, because

1 times m-reduction [i] would yield (75, 131, 938)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 326 363562 240711 433046 466839 822720 245668 221402 610415 490332 445977 > 3¹³¹ [i]