MinT - Best Known (172−53, 172, s)-Nets in Base 8

Best Known (172−53, 172, s)-Nets in Base 8

(172−53, 172, 1026)-Net over F₈ — Constructive and digital

Digital (119, 172, 1026)-net over F₈, using

t-expansion [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]

(172−53, 172, 2831)-Net over F₈ — Digital

Digital (119, 172, 2831)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−53, 172, 1311423)-Net in Base 8 — Upper bound on s

There is no (119, 172, 1311424)-net in base 8, because

1 times m-reduction [i] would yield (119, 171, 1311424)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 26815 810673 208004 692476 467078 676742 057890 513636 789441 147229 310722 019301 128998 695531 628687 834285 450429 681750 557421 689898 430998 971804 022743 300577 601426 644325 > 8¹⁷¹ [i]