MinT - Best Known (101−27, 101, s)-Nets in Base 7

Best Known (101−27, 101, s)-Nets in Base 7

(101−27, 101, 688)-Net over F₇ — Constructive and digital

Digital (74, 101, 688)-net over F₇, using

5 times m-reduction [i] based on digital (74, 106, 688)-net over F₇, using
- trace code for nets [i] based on digital (21, 53, 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]

(101−27, 101, 3386)-Net over F₇ — Digital

Digital (74, 101, 3386)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−27, 101, 2992319)-Net in Base 7 — Upper bound on s

There is no (74, 101, 2992320)-net in base 7, because

1 times m-reduction [i] would yield (74, 100, 2992320)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 3 234489 951898 277520 555935 345528 296046 792687 747659 630957 829949 739399 946929 311310 105729 > 7¹⁰⁰ [i]