MinT - Best Known (153−43, 153, s)-Nets in Base 2

Best Known (153−43, 153, s)-Nets in Base 2

(153−43, 153, 112)-Net over F₂ — Constructive and digital

Digital (110, 153, 112)-net over F₂, using

1 times m-reduction [i] based on digital (110, 154, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 77, 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]

(153−43, 153, 167)-Net over F₂ — Digital

Digital (110, 153, 167)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−43, 153, 1279)-Net in Base 2 — Upper bound on s

There is no (110, 153, 1280)-net in base 2, because

1 times m-reduction [i] would yield (110, 152, 1280)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5741 394194 522989 061069 016134 354819 462250 334801 > 2¹⁵² [i]