MinT - Best Known (52, 52+51, s)-Nets in Base 8

Best Known (52, 52+51, s)-Nets in Base 8

(52, 52+51, 130)-Net over F₈ — Constructive and digital

Digital (52, 103, 130)-net over F₈, using

1 times m-reduction [i] based on digital (52, 104, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 52, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(52, 52+51, 186)-Net over F₈ — Digital

Digital (52, 103, 186)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+51, 7017)-Net in Base 8 — Upper bound on s

There is no (52, 103, 7018)-net in base 8, because

1 times m-reduction [i] would yield (52, 102, 7018)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 130 673173 039993 626762 633336 433319 208837 631753 306600 246771 264198 970486 253313 919063 032083 477818 > 8¹⁰² [i]