MinT - Best Known (134−36, 134, s)-Nets in Base 8

Best Known (134−36, 134, s)-Nets in Base 8

(134−36, 134, 1026)-Net over F₈ — Constructive and digital

Digital (98, 134, 1026)-net over F₈, using

6 times m-reduction [i] based on digital (98, 140, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 70, 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]

(134−36, 134, 5715)-Net over F₈ — Digital

Digital (98, 134, 5715)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−36, 134, 5702094)-Net in Base 8 — Upper bound on s

There is no (98, 134, 5702095)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 10 329016 078330 578582 597533 791582 632947 817371 663467 784503 125706 525880 694985 399693 359423 044060 254065 481476 133712 581259 276500 > 8¹³⁴ [i]