MinT - Best Known (61, 61+32, s)-Nets in Base 2

Best Known (61, 61+32, s)-Nets in Base 2

(61, 61+32, 60)-Net over F₂ — Constructive and digital

Digital (61, 93, 60)-net over F₂, using

3 times m-reduction [i] based on digital (61, 96, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 48, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(61, 61+32, 71)-Net over F₂ — Digital

Digital (61, 93, 71)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+32, 359)-Net in Base 2 — Upper bound on s

There is no (61, 93, 360)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10189 404815 525602 346549 275610 > 2⁹³ [i]