MinT - Best Known (84, 84+71, s)-Nets in Base 8

Best Known (84, 84+71, s)-Nets in Base 8

(84, 84+71, 256)-Net over F₈ — Constructive and digital

Digital (84, 155, 256)-net over F₈, using

3 times m-reduction [i] based on digital (84, 158, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 79, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(84, 84+71, 362)-Net over F₈ — Digital

Digital (84, 155, 362)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+71, 18674)-Net in Base 8 — Upper bound on s

There is no (84, 155, 18675)-net in base 8, because

1 times m-reduction [i] would yield (84, 154, 18675)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 918176 014584 237759 810853 200170 060549 926190 301851 500992 655439 909224 047926 181711 888462 441500 989113 516714 490658 729841 644373 133267 304921 233480 > 8¹⁵⁴ [i]