MinT - Best Known (88−39, 88, s)-Nets in Base 8

Best Known (88−39, 88, s)-Nets in Base 8

(88−39, 88, 256)-Net over F₈ — Constructive and digital

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]

(88−39, 88, 266)-Net over F₈ — Digital

Digital (49, 88, 266)-net over F₈, using

trace code for nets [i] based on digital (5, 44, 133)-net over F₆₄, using
- net from sequence [i] based on digital (5, 132)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 133, using
    - a curve from the manYPoints database [i]

(88−39, 88, 15452)-Net in Base 8 — Upper bound on s

There is no (49, 88, 15453)-net in base 8, because

1 times m-reduction [i] would yield (49, 87, 15453)-net in base 8, but
- 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]