MinT - Best Known (180−52, 180, s)-Nets in Base 2

Best Known (180−52, 180, s)-Nets in Base 2

(180−52, 180, 112)-Net over F₂ — Constructive and digital

Digital (128, 180, 112)-net over F₂, using

10 times m-reduction [i] based on digital (128, 190, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 95, 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]

(180−52, 180, 179)-Net over F₂ — Digital

Digital (128, 180, 179)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−52, 180, 1242)-Net in Base 2 — Upper bound on s

There is no (128, 180, 1243)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 550532 034401 775394 387357 920991 789521 981572 009473 862649 > 2¹⁸⁰ [i]