MinT - Best Known (119, 119+51, s)-Nets in Base 8

Best Known (119, 119+51, s)-Nets in Base 8

(119, 119+51, 1026)-Net over F₈ — Constructive and digital

Digital (119, 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]

(119, 119+51, 3299)-Net over F₈ — Digital

Digital (119, 170, 3299)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+51, 1851025)-Net in Base 8 — Upper bound on s

There is no (119, 170, 1851026)-net in base 8, because

1 times m-reduction [i] would yield (119, 169, 1851026)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 418 995763 502054 681812 390975 773719 674891 105845 103437 496679 238601 062804 710015 078331 900934 537729 339496 590165 900914 933242 155401 794018 824446 816420 430301 951280 > 8¹⁶⁹ [i]