MinT - Best Known (112, 168, s)-Nets in Base 8

Best Known (112, 168, s)-Nets in Base 8

(112, 168, 1026)-Net over F₈ — Constructive and digital

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, 168, 1776)-Net over F₈ — Digital

Digital (112, 168, 1776)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 168, 423086)-Net in Base 8 — Upper bound on s

There is no (112, 168, 423087)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 52 376724 341475 344488 368497 569712 003933 078890 756490 558890 344305 840441 589950 563495 697863 973809 763145 276205 147435 275225 964195 401782 915027 420015 876050 802054 > 8¹⁶⁸ [i]