MinT - Best Known (167−55, 167, s)-Nets in Base 8

Best Known (167−55, 167, s)-Nets in Base 8

(167−55, 167, 1026)-Net over F₈ — Constructive and digital

Digital (112, 167, 1026)-net over F₈, using

1 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]

(167−55, 167, 1886)-Net over F₈ — Digital

Digital (112, 167, 1886)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−55, 167, 556706)-Net in Base 8 — Upper bound on s

There is no (112, 167, 556707)-net in base 8, because

1 times m-reduction [i] would yield (112, 166, 556707)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 818351 271052 629247 483153 577843 401048 955106 165368 437771 018762 957299 672030 077387 643671 369732 078038 930473 673977 222450 980581 840163 800890 519760 887359 064064 > 8¹⁶⁶ [i]