MinT - Best Known (49, 49+38, s)-Nets in Base 8

Best Known (49, 49+38, s)-Nets in Base 8

(49, 49+38, 256)-Net over F₈ — Constructive and digital

Digital (49, 87, 256)-net over F₈, using

1 times m-reduction [i] based on digital (49, 88, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 44, 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]

(49, 49+38, 276)-Net over F₈ — Digital

Digital (49, 87, 276)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+38, 15452)-Net in Base 8 — Upper bound on s

There is no (49, 87, 15453)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 709050 721481 608774 101519 782624 445969 430572 221670 878897 607589 372473 005782 746028 > 8⁸⁷ [i]