MinT - Best Known (96, 96+49, s)-Nets in Base 2

Best Known (96, 96+49, s)-Nets in Base 2

(96, 96+49, 68)-Net over F₂ — Constructive and digital

Digital (96, 145, 68)-net over F₂, using

5 times m-reduction [i] based on digital (96, 150, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 75, 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]

(96, 96+49, 104)-Net over F₂ — Digital

Digital (96, 145, 104)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 96+49, 592)-Net in Base 2 — Upper bound on s

There is no (96, 145, 593)-net in base 2, because

1 times m-reduction [i] would yield (96, 144, 593)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 22 484123 841429 921677 524347 443631 119361 775528 > 2¹⁴⁴ [i]