MinT - Best Known (38, 75, s)-Nets in Base 7

Best Known (38, 75, s)-Nets in Base 7

(38, 75, 100)-Net over F₇ — Constructive and digital

Digital (38, 75, 100)-net over F₇, using

1 times m-reduction [i] based on digital (38, 76, 100)-net over F₇, using
- trace code for nets [i] based on digital (0, 38, 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]

(38, 75, 128)-Net over F₇ — Digital

Digital (38, 75, 128)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 75, 3740)-Net in Base 7 — Upper bound on s

There is no (38, 75, 3741)-net in base 7, because

1 times m-reduction [i] would yield (38, 74, 3741)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 345 247185 500103 969136 066042 314163 841486 798010 462496 046737 569289 > 7⁷⁴ [i]