MinT - Best Known (76, 76+48, s)-Nets in Base 2

Best Known (76, 76+48, s)-Nets in Base 2

(76, 76+48, 60)-Net over F₂ — Constructive and digital

Digital (76, 124, 60)-net over F₂, using

2 times m-reduction [i] based on digital (76, 126, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 63, 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]

(76, 76+48, 67)-Net over F₂ — Digital

Digital (76, 124, 67)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+48, 318)-Net in Base 2 — Upper bound on s

There is no (76, 124, 319)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 22 522543 955408 141056 812464 161246 662149 > 2¹²⁴ [i]