MinT - Best Known (150, 150+70, s)-Nets in Base 2

Best Known (150, 150+70, s)-Nets in Base 2

(150, 150+70, 112)-Net over F₂ — Constructive and digital

Digital (150, 220, 112)-net over F₂, using

14 times m-reduction [i] based on digital (150, 234, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 117, 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]

(150, 150+70, 168)-Net over F₂ — Digital

Digital (150, 220, 168)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+70, 1034)-Net in Base 2 — Upper bound on s

There is no (150, 220, 1035)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 730838 235226 301917 447773 627703 525953 803191 971635 429196 479028 369984 > 2²²⁰ [i]