MinT - Best Known (111, 111+41, s)-Nets in Base 2

Best Known (111, 111+41, s)-Nets in Base 2

(111, 111+41, 135)-Net over F₂ — Constructive and digital

Digital (111, 152, 135)-net over F₂, using

1 times m-reduction [i] based on digital (111, 153, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 51, 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]

(111, 111+41, 184)-Net over F₂ — Digital

Digital (111, 152, 184)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+41, 1527)-Net in Base 2 — Upper bound on s

There is no (111, 152, 1528)-net in base 2, because

1 times m-reduction [i] would yield (111, 151, 1528)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2890 889085 721919 406333 405957 416641 485566 846441 > 2¹⁵¹ [i]