MinT - Best Known (153−53, 153, s)-Nets in Base 2

Best Known (153−53, 153, s)-Nets in Base 2

(153−53, 153, 68)-Net over F₂ — Constructive and digital

Digital (100, 153, 68)-net over F₂, using

5 times m-reduction [i] based on digital (100, 158, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 79, 34)-net over F₄, using
  - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
      - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(153−53, 153, 103)-Net over F₂ — Digital

Digital (100, 153, 103)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−53, 153, 569)-Net in Base 2 — Upper bound on s

There is no (100, 153, 570)-net in base 2, because

1 times m-reduction [i] would yield (100, 152, 570)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5823 183054 551272 130945 753274 727745 555149 866664 > 2¹⁵² [i]