MinT - Best Known (70, 70+25, s)-Nets in Base 7

Best Known (70, 70+25, s)-Nets in Base 7

(70, 70+25, 688)-Net over F₇ — Constructive and digital

Digital (70, 95, 688)-net over F₇, using

3 times m-reduction [i] based on digital (70, 98, 688)-net over F₇, using
- trace code for nets [i] based on digital (21, 49, 344)-net over F₄₉, using
  - net from sequence [i] based on digital (21, 343)-sequence over F₄₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 21 and N(F) ≥ 344, using
      - the Hermitian function field over F₄₉ [i]

(70, 70+25, 3629)-Net over F₇ — Digital

Digital (70, 95, 3629)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+25, 3674040)-Net in Base 7 — Upper bound on s

There is no (70, 95, 3674041)-net in base 7, because

1 times m-reduction [i] would yield (70, 94, 3674041)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 27 492653 623358 967255 564867 227633 590079 244281 574130 233806 111472 235643 051015 562721 > 7⁹⁴ [i]