MinT - Best Known (173−57, 173, s)-Nets in Base 8

Best Known (173−57, 173, s)-Nets in Base 8

(173−57, 173, 1026)-Net over F₈ — Constructive and digital

Digital (116, 173, 1026)-net over F₈, using

8¹ times duplication [i] based on digital (115, 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]

(173−57, 173, 1940)-Net over F₈ — Digital

Digital (116, 173, 1940)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−57, 173, 569437)-Net in Base 8 — Upper bound on s

There is no (116, 173, 569438)-net in base 8, because

1 times m-reduction [i] would yield (116, 172, 569438)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 214525 274847 318521 685510 095991 240240 942792 465230 534382 420747 694198 933617 945416 861660 709042 180831 046717 833564 951892 141759 101390 683156 052254 068134 475664 922417 > 8¹⁷² [i]