MinT - Best Known (173−55, 173, s)-Nets in Base 8

Best Known (173−55, 173, s)-Nets in Base 8

(173−55, 173, 1026)-Net over F₈ — Constructive and digital

Digital (118, 173, 1026)-net over F₈, using

8¹ times duplication [i] based on digital (117, 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]

(173−55, 173, 2369)-Net over F₈ — Digital

Digital (118, 173, 2369)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−55, 173, 883727)-Net in Base 8 — Upper bound on s

There is no (118, 173, 883728)-net in base 8, because

1 times m-reduction [i] would yield (118, 172, 883728)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 214531 255377 581376 486341 849451 720146 476322 023492 093139 116807 158816 341704 263867 020305 375122 884105 196223 487457 606814 240108 508213 849335 081810 128728 621540 551232 > 8¹⁷² [i]