MinT - Best Known (226−72, 226, s)-Nets in Base 2

Best Known (226−72, 226, s)-Nets in Base 2

(226−72, 226, 112)-Net over F₂ — Constructive and digital

Digital (154, 226, 112)-net over F₂, using

16 times m-reduction [i] based on digital (154, 242, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 121, 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]

(226−72, 226, 172)-Net over F₂ — Digital

Digital (154, 226, 172)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−72, 226, 1055)-Net in Base 2 — Upper bound on s

There is no (154, 226, 1056)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 109 094356 094406 759375 194568 467713 358182 172790 480403 502924 403898 956064 > 2²²⁶ [i]