MinT - Best Known (226−67, 226, s)-Nets in Base 2

Best Known (226−67, 226, s)-Nets in Base 2

(226−67, 226, 112)-Net over F₂ — Constructive and digital

Digital (159, 226, 112)-net over F₂, using

26 times m-reduction [i] based on digital (159, 252, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 126, 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]

(226−67, 226, 204)-Net over F₂ — Digital

Digital (159, 226, 204)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−67, 226, 1437)-Net in Base 2 — Upper bound on s

There is no (159, 226, 1438)-net in base 2, because

1 times m-reduction [i] would yield (159, 225, 1438)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 55 026386 645007 458053 832641 835612 041315 919533 223826 486656 927447 827828 > 2²²⁵ [i]