MinT - Best Known (171−57, 171, s)-Nets in Base 8

Best Known (171−57, 171, s)-Nets in Base 8

(171−57, 171, 1026)-Net over F₈ — Constructive and digital

Digital (114, 171, 1026)-net over F₈, using

1 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]

(171−57, 171, 1803)-Net over F₈ — Digital

Digital (114, 171, 1803)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(171−57, 171, 490837)-Net in Base 8 — Upper bound on s

There is no (114, 171, 490838)-net in base 8, because

1 times m-reduction [i] would yield (114, 170, 490838)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3352 021673 381593 309862 125601 599478 696921 124842 303791 165320 564894 167079 551320 142164 287009 157860 105731 025691 686639 604797 724817 876204 159238 370698 039360 463704 > 8¹⁷⁰ [i]