MinT - Best Known (71, 71+57, s)-Nets in Base 8

Best Known (71, 71+57, s)-Nets in Base 8

(71, 71+57, 354)-Net over F₈ — Constructive and digital

Digital (71, 128, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 64, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(71, 71+57, 20122)-Net in Base 8 — Upper bound on s

There is no (71, 128, 20123)-net in base 8, because

1 times m-reduction [i] would yield (71, 127, 20123)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 926839 495565 278390 803144 528110 113409 526806 483916 754707 712201 452699 306342 983052 737309 202389 643123 069858 120829 118816 > 8¹²⁷ [i]