MinT - Best Known (151, 151+82, s)-Nets in Base 2

Best Known (151, 151+82, s)-Nets in Base 2

(151, 151+82, 112)-Net over F₂ — Constructive and digital

Digital (151, 233, 112)-net over F₂, using

3 times m-reduction [i] based on digital (151, 236, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 118, 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]

(151, 151+82, 140)-Net over F₂ — Digital

Digital (151, 233, 140)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 151+82, 770)-Net in Base 2 — Upper bound on s

There is no (151, 233, 771)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 14399 107052 755358 452927 525119 256439 684027 030943 986651 897553 953153 326464 > 2²³³ [i]