MinT - Best Known (71, 71+63, s)-Nets in Base 8

Best Known (71, 71+63, s)-Nets in Base 8

(71, 71+63, 208)-Net over F₈ — Constructive and digital

Digital (71, 134, 208)-net over F₈, using

2 times m-reduction [i] based on digital (71, 136, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 68, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(71, 71+63, 287)-Net over F₈ — Digital

Digital (71, 134, 287)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+63, 13269)-Net in Base 8 — Upper bound on s

There is no (71, 134, 13270)-net in base 8, because

1 times m-reduction [i] would yield (71, 133, 13270)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 293314 553538 047947 111481 091019 896940 560508 018695 064628 607534 102775 685608 578513 177044 747974 473215 494252 592194 491176 842592 > 8¹³³ [i]