MinT - Best Known (109, 109+52, s)-Nets in Base 8

Best Known (109, 109+52, s)-Nets in Base 8

(109, 109+52, 1026)-Net over F₈ — Constructive and digital

Digital (109, 161, 1026)-net over F₈, using

1 times m-reduction [i] based on digital (109, 162, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 81, 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]

(109, 109+52, 2038)-Net over F₈ — Digital

Digital (109, 161, 2038)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 109+52, 589378)-Net in Base 8 — Upper bound on s

There is no (109, 161, 589379)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 24 974784 283917 497448 976499 263919 828172 488909 521695 945448 831226 705700 055790 127962 730191 368312 525025 581082 013926 828938 638026 231406 727579 020794 231272 > 8¹⁶¹ [i]