MinT - Best Known (121−55, 121, s)-Nets in Base 8

Best Known (121−55, 121, s)-Nets in Base 8

(121−55, 121, 256)-Net over F₈ — Constructive and digital

Digital (66, 121, 256)-net over F₈, using

1 times m-reduction [i] based on digital (66, 122, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 61, 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]

(121−55, 121, 302)-Net over F₈ — Digital

Digital (66, 121, 302)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−55, 121, 16091)-Net in Base 8 — Upper bound on s

There is no (66, 121, 16092)-net in base 8, because

1 times m-reduction [i] would yield (66, 120, 16092)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 351841 468714 364428 709907 020714 583910 732424 241211 796223 582050 505092 528515 334260 952664 075488 227727 766289 854979 > 8¹²⁰ [i]