MinT - Best Known (132−36, 132, s)-Nets in Base 8

Best Known (132−36, 132, s)-Nets in Base 8

(132−36, 132, 1026)-Net over F₈ — Constructive and digital

Digital (96, 132, 1026)-net over F₈, using

4 times m-reduction [i] based on digital (96, 136, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 68, 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]

(132−36, 132, 5077)-Net over F₈ — Digital

Digital (96, 132, 5077)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(132−36, 132, 4525753)-Net in Base 8 — Upper bound on s

There is no (96, 132, 4525754)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 161391 186458 771300 117964 732311 623831 970758 722800 224586 976343 856395 144101 794087 780969 356517 426272 076122 943946 673222 011140 > 8¹³² [i]