MinT - Best Known (145−44, 145, s)-Nets in Base 8

Best Known (145−44, 145, s)-Nets in Base 8

(145−44, 145, 1026)-Net over F₈ — Constructive and digital

Digital (101, 145, 1026)-net over F₈, using

1 times m-reduction [i] based on digital (101, 146, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 73, 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]

(145−44, 145, 2699)-Net over F₈ — Digital

Digital (101, 145, 2699)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−44, 145, 1158600)-Net in Base 8 — Upper bound on s

There is no (101, 145, 1158601)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 88725 523747 520039 342204 129949 087729 585317 470875 666916 136039 743051 772694 681561 403073 613244 116933 615014 077203 964870 368266 839056 391344 > 8¹⁴⁵ [i]