MinT - Best Known (132, 132+53, s)-Nets in Base 2

Best Known (132, 132+53, s)-Nets in Base 2

(132, 132+53, 112)-Net over F₂ — Constructive and digital

Digital (132, 185, 112)-net over F₂, using

13 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+53, 186)-Net over F₂ — Digital

Digital (132, 185, 186)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(132, 132+53, 1386)-Net in Base 2 — Upper bound on s

There is no (132, 185, 1387)-net in base 2, because

1 times m-reduction [i] would yield (132, 184, 1387)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 24 763838 159291 209026 731818 743197 588710 331088 997689 497726 > 2¹⁸⁴ [i]