MinT - Best Known (258−49, 258, s)-Nets in Base 2

Best Known (258−49, 258, s)-Nets in Base 2

(258−49, 258, 294)-Net over F₂ — Constructive and digital

Digital (209, 258, 294)-net over F₂, using

trace code for nets [i] based on digital (37, 86, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(258−49, 258, 754)-Net over F₂ — Digital

Digital (209, 258, 754)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(258−49, 258, 16366)-Net in Base 2 — Upper bound on s

There is no (209, 258, 16367)-net in base 2, because

1 times m-reduction [i] would yield (209, 257, 16367)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 231799 854622 277012 332211 661697 327566 076742 578565 947955 724052 628831 113035 941666 > 2²⁵⁷ [i]