MinT - Best Known (117, 117+53, s)-Nets in Base 8

Best Known (117, 117+53, s)-Nets in Base 8

(117, 117+53, 1026)-Net over F₈ — Constructive and digital

Digital (117, 170, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 170, 1026)-net over F₈, using
- 2 times m-reduction [i] based on digital (114, 172, 1026)-net over F₈, using
  - trace code for nets [i] based on digital (28, 86, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(117, 117+53, 2615)-Net over F₈ — Digital

Digital (117, 170, 2615)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+53, 1117567)-Net in Base 8 — Upper bound on s

There is no (117, 170, 1117568)-net in base 8, because

1 times m-reduction [i] would yield (117, 169, 1117568)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 419 002623 008528 229023 741276 227823 418608 691243 323682 821698 102777 924355 828646 581151 230489 708281 072432 740111 676506 121849 167261 200796 424474 234528 924234 408009 > 8¹⁶⁹ [i]