MinT - Best Known (139−59, 139, s)-Nets in Base 2

Best Known (139−59, 139, s)-Nets in Base 2

(139−59, 139, 54)-Net over F₂ — Constructive and digital

Digital (80, 139, 54)-net over F₂, using

1 times m-reduction [i] based on digital (80, 140, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 70, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]

(139−59, 139, 60)-Net over F₂ — Digital

Digital (80, 139, 60)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(139−59, 139, 275)-Net in Base 2 — Upper bound on s

There is no (80, 139, 276)-net in base 2, because

1 times m-reduction [i] would yield (80, 138, 276)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 367266 152841 991796 289004 622202 269988 065088 > 2¹³⁸ [i]