MinT - Best Known (134−37, 134, s)-Nets in Base 8

Best Known (134−37, 134, s)-Nets in Base 8

(134−37, 134, 1026)-Net over F₈ — Constructive and digital

Digital (97, 134, 1026)-net over F₈, using

4 times m-reduction [i] based on digital (97, 138, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 69, 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]

(134−37, 134, 4708)-Net over F₈ — Digital

Digital (97, 134, 4708)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−37, 134, 5079987)-Net in Base 8 — Upper bound on s

There is no (97, 134, 5079988)-net in base 8, because

1 times m-reduction [i] would yield (97, 133, 5079988)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 291127 383516 523204 769042 503033 369241 327337 621167 322579 773385 400911 619585 492903 044119 584375 968822 729225 421985 592389 204421 > 8¹³³ [i]