MinT - Best Known (42, 42+31, s)-Nets in Base 8

Best Known (42, 42+31, s)-Nets in Base 8

(42, 42+31, 256)-Net over F₈ — Constructive and digital

Digital (42, 73, 256)-net over F₈, using

1 times m-reduction [i] based on digital (42, 74, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 37, 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]

(42, 42+31, 277)-Net over F₈ — Digital

Digital (42, 73, 277)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+31, 19828)-Net in Base 8 — Upper bound on s

There is no (42, 73, 19829)-net in base 8, because

1 times m-reduction [i] would yield (42, 72, 19829)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 105313 913395 658799 668947 663597 069446 142222 066297 799725 943562 997392 > 8⁷² [i]