MinT - Best Known (132, 132+62, s)-Nets in Base 2

Best Known (132, 132+62, s)-Nets in Base 2

(132, 132+62, 112)-Net over F₂ — Constructive and digital

Digital (132, 194, 112)-net over F₂, using

4 times m-reduction [i] based on digital (132, 198, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 99, 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]

(132, 132+62, 150)-Net over F₂ — Digital

Digital (132, 194, 150)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 132+62, 905)-Net in Base 2 — Upper bound on s

There is no (132, 194, 906)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 25626 789081 133056 385781 330944 484167 490741 463033 480126 020928 > 2¹⁹⁴ [i]