MinT - Best Known (171−75, 171, s)-Nets in Base 3

Best Known (171−75, 171, s)-Nets in Base 3

(171−75, 171, 80)-Net over F₃ — Constructive and digital

Digital (96, 171, 80)-net over F₃, using

5 times m-reduction [i] based on digital (96, 176, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 88, 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]

(171−75, 171, 126)-Net over F₃ — Digital

Digital (96, 171, 126)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−75, 171, 1104)-Net in Base 3 — Upper bound on s

There is no (96, 171, 1105)-net in base 3, because

1 times m-reduction [i] would yield (96, 170, 1105)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1315 942731 974278 726605 074686 075402 752513 902710 672767 107664 229442 021718 576972 212499 > 3¹⁷⁰ [i]