MinT - Best Known (54, 54+50, s)-Nets in Base 8

Best Known (54, 54+50, s)-Nets in Base 8

(54, 54+50, 160)-Net over F₈ — Constructive and digital

Digital (54, 104, 160)-net over F₈, using

2 times m-reduction [i] based on digital (54, 106, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 53, 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]

(54, 54+50, 212)-Net over F₈ — Digital

Digital (54, 104, 212)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+50, 8290)-Net in Base 8 — Upper bound on s

There is no (54, 104, 8291)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 8362 548137 221138 871718 127907 519091 102340 822823 334784 320522 562779 517957 841461 253573 455526 867160 > 8¹⁰⁴ [i]