MinT - Best Known (96, 96+39, s)-Nets in Base 8

Best Known (96, 96+39, s)-Nets in Base 8

(96, 96+39, 1026)-Net over F₈ — Constructive and digital

Digital (96, 135, 1026)-net over F₈, using

1 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]

(96, 96+39, 3487)-Net over F₈ — Digital

Digital (96, 135, 3487)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 96+39, 2650186)-Net in Base 8 — Upper bound on s

There is no (96, 135, 2650187)-net in base 8, because

1 times m-reduction [i] would yield (96, 134, 2650187)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 10 329004 795040 589292 190540 606666 074148 269342 560504 899196 656044 591266 421389 782233 585150 317522 299716 672210 831361 570528 482752 > 8¹³⁴ [i]