MinT - Best Known (82−36, 82, s)-Nets in Base 8

Best Known (82−36, 82, s)-Nets in Base 8

(82−36, 82, 256)-Net over F₈ — Constructive and digital

Digital (46, 82, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 41, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(82−36, 82, 266)-Net over F₈ — Digital

Digital (46, 82, 266)-net over F₈, using

trace code for nets [i] based on digital (5, 41, 133)-net over F₆₄, using
- net from sequence [i] based on digital (5, 132)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 133, using
    - a curve from the manYPoints database [i]

(82−36, 82, 14020)-Net in Base 8 — Upper bound on s

There is no (46, 82, 14021)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 113 139521 054246 300780 377700 448484 017299 508403 818380 038058 280034 126041 134392 > 8⁸² [i]