MinT - Best Known (241−83, 241, s)-Nets in Base 2

Best Known (241−83, 241, s)-Nets in Base 2

(241−83, 241, 112)-Net over F₂ — Constructive and digital

Digital (158, 241, 112)-net over F₂, using

9 times m-reduction [i] based on digital (158, 250, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 125, 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]

(241−83, 241, 152)-Net over F₂ — Digital

Digital (158, 241, 152)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−83, 241, 874)-Net in Base 2 — Upper bound on s

There is no (158, 241, 875)-net in base 2, because

1 times m-reduction [i] would yield (158, 240, 875)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 837962 223808 942805 750939 227266 857501 411928 911543 517573 336254 249991 396236 > 2²⁴⁰ [i]