MinT - Best Known (100−48, 100, s)-Nets in Base 8

Best Known (100−48, 100, s)-Nets in Base 8

(100−48, 100, 160)-Net over F₈ — Constructive and digital

Digital (52, 100, 160)-net over F₈, using

2 times m-reduction [i] based on digital (52, 102, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 51, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(100−48, 100, 206)-Net over F₈ — Digital

Digital (52, 100, 206)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(100−48, 100, 8097)-Net in Base 8 — Upper bound on s

There is no (52, 100, 8098)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 041267 987844 370466 558833 297587 111402 720176 495269 579126 296319 329780 743896 312192 016760 831404 > 8¹⁰⁰ [i]