MinT - Best Known (82, 82+26, s)-Nets in Base 7

Best Known (82, 82+26, s)-Nets in Base 7

(82, 82+26, 697)-Net over F₇ — Constructive and digital

Digital (82, 108, 697)-net over F₇, using

(u,Â u+v)-construction [i] based on
1. digital (1, 14, 9)-net over F₇, using
  - net from sequence [i] based on digital (1, 8)-sequence over F₇, using
    - Niederreiter sequence [i]
2. digital (68, 94, 688)-net over F₇, using
  - trace code for nets [i] based on digital (21, 47, 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]

(82, 82+26, 7603)-Net over F₇ — Digital

Digital (82, 108, 7603)-net over F₇, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+26, large)-Net in Base 7 — Upper bound on s

There is no (82, 108, large)-net in base 7, because

24 times m-reduction [i] would yield (82, 84, large)-net in base 7, but
- mutually orthogonal hypercube bound [i]