MinT - Best Known (224−79, 224, s)-Nets in Base 2

Best Known (224−79, 224, s)-Nets in Base 2

(224−79, 224, 112)-Net over F₂ — Constructive and digital

Digital (145, 224, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 112, 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]

(224−79, 224, 135)-Net over F₂ — Digital

Digital (145, 224, 135)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(224−79, 224, 754)-Net in Base 2 — Upper bound on s

There is no (145, 224, 755)-net in base 2, because

1 times m-reduction [i] would yield (145, 223, 755)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13 990515 968127 644020 613990 481580 087509 080212 191098 590389 904614 324968 > 2²²³ [i]