MinT - Best Known (115, 115+53, s)-Nets in Base 8

Best Known (115, 115+53, s)-Nets in Base 8

(115, 115+53, 1026)-Net over F₈ — Constructive and digital

Digital (115, 168, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 168, 1026)-net over F₈, using
- 4 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]

(115, 115+53, 2416)-Net over F₈ — Digital

Digital (115, 168, 2416)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+53, 952366)-Net in Base 8 — Upper bound on s

There is no (115, 168, 952367)-net in base 8, because

1 times m-reduction [i] would yield (115, 167, 952367)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 546890 156244 085623 391847 172959 621237 561729 078603 277122 434821 485098 374547 005997 901123 106874 192534 364269 793260 697145 341659 959283 505503 529037 928993 834570 > 8¹⁶⁷ [i]