MinT - Best Known (226−80, 226, s)-Nets in Base 2

Best Known (226−80, 226, s)-Nets in Base 2

(226−80, 226, 112)-Net over F₂ — Constructive and digital

Digital (146, 226, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 113, 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]

(226−80, 226, 135)-Net over F₂ — Digital

Digital (146, 226, 135)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−80, 226, 734)-Net in Base 2 — Upper bound on s

There is no (146, 226, 735)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 111 969366 572453 885396 193272 768287 711962 407237 207746 580960 337525 807030 > 2²²⁶ [i]