MinT - Best Known (147, 147+75, s)-Nets in Base 2

Best Known (147, 147+75, s)-Nets in Base 2

(147, 147+75, 112)-Net over F₂ — Constructive and digital

Digital (147, 222, 112)-net over F₂, using

6 times m-reduction [i] based on digital (147, 228, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 114, 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]

(147, 147+75, 148)-Net over F₂ — Digital

Digital (147, 222, 148)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+75, 866)-Net in Base 2 — Upper bound on s

There is no (147, 222, 867)-net in base 2, because

1 times m-reduction [i] would yield (147, 221, 867)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3 395423 304077 336547 992842 604191 865802 688853 044878 148773 862626 494192 > 2²²¹ [i]