MinT - Best Known (65−32, 65, s)-Nets in Base 7

Best Known (65−32, 65, s)-Nets in Base 7

(65−32, 65, 100)-Net over F₇ — Constructive and digital

Digital (33, 65, 100)-net over F₇, using

1 times m-reduction [i] based on digital (33, 66, 100)-net over F₇, using
- trace code for nets [i] based on digital (0, 33, 50)-net over F₄₉, using
  - net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
      - the rational function field F₄₉(x) [i]
    - Niederreiter sequence [i]

(65−32, 65, 115)-Net over F₇ — Digital

Digital (33, 65, 115)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(65−32, 65, 3063)-Net in Base 7 — Upper bound on s

There is no (33, 65, 3064)-net in base 7, because

the generalized Rao bound for nets shows that 7^mÂ â‰¥ 8 578552 728537 334336 107178 112066 517589 949523 504529 181185 > 7⁶⁵ [i]