MinT - Best Known (141, 141+71, s)-Nets in Base 2

Best Known (141, 141+71, s)-Nets in Base 2

(141, 141+71, 112)-Net over F₂ — Constructive and digital

Digital (141, 212, 112)-net over F₂, using

4 times m-reduction [i] based on digital (141, 216, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 108, 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]

(141, 141+71, 145)-Net over F₂ — Digital

Digital (141, 212, 145)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 141+71, 857)-Net in Base 2 — Upper bound on s

There is no (141, 212, 858)-net in base 2, because

1 times m-reduction [i] would yield (141, 211, 858)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3389 523906 741953 313150 814376 132773 925431 588827 308710 405842 404688 > 2²¹¹ [i]