MinT - Best Known (112, 112+43, s)-Nets in Base 8

Best Known (112, 112+43, s)-Nets in Base 8

(112, 112+43, 1026)-Net over F₈ — Constructive and digital

Digital (112, 155, 1026)-net over F₈, using

13 times m-reduction [i] based on digital (112, 168, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 84, 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]

(112, 112+43, 5097)-Net over F₈ — Digital

Digital (112, 155, 5097)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+43, 5200598)-Net in Base 8 — Upper bound on s

There is no (112, 155, 5200599)-net in base 8, because

1 times m-reduction [i] would yield (112, 154, 5200599)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 908538 288646 564364 168249 713685 246319 975027 840275 752404 623094 780947 857468 274794 435301 394659 561092 461893 544929 006938 301852 720648 277812 210394 > 8¹⁵⁴ [i]