MinT - Best Known (135, 135+62, s)-Nets in Base 2

Best Known (135, 135+62, s)-Nets in Base 2

(135, 135+62, 112)-Net over F₂ — Constructive and digital

Digital (135, 197, 112)-net over F₂, using

7 times m-reduction [i] based on digital (135, 204, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 102, 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]

(135, 135+62, 157)-Net over F₂ — Digital

Digital (135, 197, 157)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+62, 971)-Net in Base 2 — Upper bound on s

There is no (135, 197, 972)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 205527 806677 720356 759516 792287 767338 878317 989026 532509 121040 > 2¹⁹⁷ [i]