MinT - Best Known (241−85, 241, s)-Nets in Base 2

Best Known (241−85, 241, s)-Nets in Base 2

(241−85, 241, 112)-Net over F₂ — Constructive and digital

Digital (156, 241, 112)-net over F₂, using

5 times m-reduction [i] based on digital (156, 246, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 123, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(241−85, 241, 144)-Net over F₂ — Digital

Digital (156, 241, 144)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−85, 241, 806)-Net in Base 2 — Upper bound on s

There is no (156, 241, 807)-net in base 2, because

1 times m-reduction [i] would yield (156, 240, 807)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 819570 336972 663368 304339 673908 820064 676713 076537 451007 419986 752833 524160 > 2²⁴⁰ [i]