MinT - Best Known (170−55, 170, s)-Nets in Base 8

Best Known (170−55, 170, s)-Nets in Base 8

(170−55, 170, 1026)-Net over F₈ — Constructive and digital

Digital (115, 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]

(170−55, 170, 2114)-Net over F₈ — Digital

Digital (115, 170, 2114)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−55, 170, 701411)-Net in Base 8 — Upper bound on s

There is no (115, 170, 701412)-net in base 8, because

1 times m-reduction [i] would yield (115, 169, 701412)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 419 007957 273282 709033 376918 552023 548444 683332 823205 559010 833516 670583 866844 268970 462564 474121 432066 726139 532993 295919 424922 328730 059281 998043 586200 618300 > 8¹⁶⁹ [i]