MinT - Best Known (169−48, 169, s)-Nets in Base 8

Best Known (169−48, 169, s)-Nets in Base 8

(169−48, 169, 1026)-Net over F₈ — Constructive and digital

Digital (121, 169, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 169, 1026)-net over F₈, using
- 3 times m-reduction [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]

(169−48, 169, 4661)-Net over F₈ — Digital

Digital (121, 169, 4661)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−48, 169, 3202737)-Net in Base 8 — Upper bound on s

There is no (121, 169, 3202738)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 418 995904 164868 082224 562245 370100 658722 578888 204004 932397 116357 971043 253591 592531 505407 947175 894490 546665 050495 730242 768756 754107 415460 826631 803036 524236 > 8¹⁶⁹ [i]