MinT - Best Known (163−53, 163, s)-Nets in Base 8

Best Known (163−53, 163, s)-Nets in Base 8

(163−53, 163, 1026)-Net over F₈ — Constructive and digital

Digital (110, 163, 1026)-net over F₈, using

1 times m-reduction [i] based on digital (110, 164, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 82, 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]

(163−53, 163, 1983)-Net over F₈ — Digital

Digital (110, 163, 1983)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−53, 163, 638453)-Net in Base 8 — Upper bound on s

There is no (110, 163, 638454)-net in base 8, because

1 times m-reduction [i] would yield (110, 162, 638454)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 199 795954 507592 705066 451927 993006 193515 806566 491021 897895 066366 163865 943526 082436 395296 871121 241718 044187 062034 877589 112427 528112 078363 560684 064936 > 8¹⁶² [i]