MinT - Best Known (180, 180+76, s)-Nets in Base 2

Best Known (180, 180+76, s)-Nets in Base 2

(180, 180+76, 135)-Net over F₂ — Constructive and digital

Digital (180, 256, 135)-net over F₂, using

2¹ times duplication [i] based on digital (179, 255, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 85, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(180, 180+76, 226)-Net over F₂ — Digital

Digital (180, 256, 226)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+76, 1546)-Net in Base 2 — Upper bound on s

There is no (180, 256, 1547)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 116112 211192 953433 156342 709092 317416 509751 702459 011560 016656 351515 136682 395680 > 2²⁵⁶ [i]