MinT - Best Known (226−76, 226, s)-Nets in Base 2

Best Known (226−76, 226, s)-Nets in Base 2

(226−76, 226, 112)-Net over F₂ — Constructive and digital

Digital (150, 226, 112)-net over F₂, using

8 times m-reduction [i] based on digital (150, 234, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 117, 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]

(226−76, 226, 152)-Net over F₂ — Digital

Digital (150, 226, 152)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−76, 226, 872)-Net in Base 2 — Upper bound on s

There is no (150, 226, 873)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 111 651876 070674 010694 930474 212678 850622 384863 407898 805991 104425 237708 > 2²²⁶ [i]