MinT - Best Known (170−48, 170, s)-Nets in Base 2

Best Known (170−48, 170, s)-Nets in Base 2

(170−48, 170, 112)-Net over F₂ — Constructive and digital

Digital (122, 170, 112)-net over F₂, using

8 times m-reduction [i] based on digital (122, 178, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 89, 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]

(170−48, 170, 180)-Net over F₂ — Digital

Digital (122, 170, 180)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−48, 170, 1294)-Net in Base 2 — Upper bound on s

There is no (122, 170, 1295)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1514 645403 667712 588565 918502 226661 534630 260561 657392 > 2¹⁷⁰ [i]