MinT - Best Known (123, 170, s)-Nets in Base 8

Best Known (123, 170, s)-Nets in Base 8

(123, 170, 1026)-Net over F₈ — Constructive and digital

Digital (123, 170, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 170, 1026)-net over F₈, using
- 2 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]

(123, 170, 5616)-Net over F₈ — Digital

Digital (123, 170, 5616)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 170, 5822444)-Net in Base 8 — Upper bound on s

There is no (123, 170, 5822445)-net in base 8, because

1 times m-reduction [i] would yield (123, 169, 5822445)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 418 995231 225952 815023 973445 887532 358768 747185 731107 537447 467028 331413 724172 891659 399511 363938 835741 491148 345213 072084 715663 649922 704365 124542 249470 437008 > 8¹⁶⁹ [i]