MinT - Best Known (137−36, 137, s)-Nets in Base 8

Best Known (137−36, 137, s)-Nets in Base 8

(137−36, 137, 1026)-Net over F₈ — Constructive and digital

Digital (101, 137, 1026)-net over F₈, using

9 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]

(137−36, 137, 6827)-Net over F₈ — Digital

Digital (101, 137, 6827)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−36, 137, 8063983)-Net in Base 8 — Upper bound on s

There is no (101, 137, 8063984)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5288 448336 359857 843027 860154 248260 655648 298090 201983 592434 201781 868444 169562 418526 082630 816711 103316 053003 668086 459414 747670 > 8¹³⁷ [i]