MinT - Best Known (144−49, 144, s)-Nets in Base 2

Best Known (144−49, 144, s)-Nets in Base 2

(144−49, 144, 68)-Net over F₂ — Constructive and digital

Digital (95, 144, 68)-net over F₂, using

4 times m-reduction [i] based on digital (95, 148, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 74, 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]

(144−49, 144, 102)-Net over F₂ — Digital

Digital (95, 144, 102)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−49, 144, 574)-Net in Base 2 — Upper bound on s

There is no (95, 144, 575)-net in base 2, because

1 times m-reduction [i] would yield (95, 143, 575)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11 172113 971430 220579 902212 069879 938593 998261 > 2¹⁴³ [i]