MinT - Best Known (108−29, 108, s)-Nets in Base 7

Best Known (108−29, 108, s)-Nets in Base 7

(108−29, 108, 688)-Net over F₇ — Constructive and digital

Digital (79, 108, 688)-net over F₇, using

t-expansion [i] based on digital (76, 108, 688)-net over F₇, using
- 2 times m-reduction [i] based on digital (76, 110, 688)-net over F₇, using
  - trace code for nets [i] based on digital (21, 55, 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]

(108−29, 108, 3438)-Net over F₇ — Digital

Digital (79, 108, 3438)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(108−29, 108, 2899137)-Net in Base 7 — Upper bound on s

There is no (79, 108, 2899138)-net in base 7, because

1 times m-reduction [i] would yield (79, 107, 2899138)-net in base 7, but
- the generalized Rao bound for nets shows that 7^mÂ â‰¥ 2 663741 743193 673900 094183 155950 571365 262350 123692 601384 938527 895074 377728 331443 591646 546077 > 7¹⁰⁷ [i]