MinT - Best Known (129−49, 129, s)-Nets in Base 2

Best Known (129−49, 129, s)-Nets in Base 2

(129−49, 129, 66)-Net over F₂ — Constructive and digital

Digital (80, 129, 66)-net over F₂, using

1 times m-reduction [i] based on digital (80, 130, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 65, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(129−49, 129, 73)-Net over F₂ — Digital

Digital (80, 129, 73)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−49, 129, 361)-Net in Base 2 — Upper bound on s

There is no (80, 129, 362)-net in base 2, because

1 times m-reduction [i] would yield (80, 128, 362)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 358 973609 277700 752288 209096 708336 066102 > 2¹²⁸ [i]