MinT - Best Known (154−47, 154, s)-Nets in Base 8

Best Known (154−47, 154, s)-Nets in Base 8

(154−47, 154, 1026)-Net over F₈ — Constructive and digital

Digital (107, 154, 1026)-net over F₈, using

4 times m-reduction [i] based on digital (107, 158, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 79, 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]

(154−47, 154, 2736)-Net over F₈ — Digital

Digital (107, 154, 2736)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−47, 154, 1370456)-Net in Base 8 — Upper bound on s

There is no (107, 154, 1370457)-net in base 8, because

1 times m-reduction [i] would yield (107, 153, 1370457)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 488569 529351 615348 859739 409206 436552 834193 805594 343792 137913 107821 688844 010030 121009 528667 252503 595796 147759 388264 599038 441691 845256 903592 > 8¹⁵³ [i]