MinT - Best Known (119−53, 119, s)-Nets in Base 8

Best Known (119−53, 119, s)-Nets in Base 8

(119−53, 119, 256)-Net over F₈ — Constructive and digital

Digital (66, 119, 256)-net over F₈, using

3 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]

(119−53, 119, 325)-Net over F₈ — Digital

Digital (66, 119, 325)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(119−53, 119, 18900)-Net in Base 8 — Upper bound on s

There is no (66, 119, 18901)-net in base 8, because

1 times m-reduction [i] would yield (66, 118, 18901)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 36746 351101 167735 100891 982170 400037 051029 404082 270387 080612 575100 077299 190217 709808 182848 153027 766298 224080 > 8¹¹⁸ [i]