MinT - Best Known (139−38, 139, s)-Nets in Base 8

Best Known (139−38, 139, s)-Nets in Base 8

(139−38, 139, 1026)-Net over F₈ — Constructive and digital

Digital (101, 139, 1026)-net over F₈, using

7 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]

(139−38, 139, 5189)-Net over F₈ — Digital

Digital (101, 139, 5189)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−38, 139, 4580707)-Net in Base 8 — Upper bound on s

There is no (101, 139, 4580708)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 338461 128766 142879 296112 505759 780108 697719 202460 168939 663079 604192 230661 812896 222049 381631 055720 182168 100035 536873 592229 892414 > 8¹³⁹ [i]