MinT - Best Known (81, 81+27, s)-Nets in Base 7

Best Known (81, 81+27, s)-Nets in Base 7

(81, 81+27, 688)-Net over F₇ — Constructive and digital

Digital (81, 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]

(81, 81+27, 5709)-Net over F₇ — Digital

Digital (81, 108, 5709)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+27, large)-Net in Base 7 — Upper bound on s

There is no (81, 108, large)-net in base 7, because

25 times m-reduction [i] would yield (81, 83, large)-net in base 7, but
- mutually orthogonal hypercube bound [i]