MinT - Best Known (111, 111+42, s)-Nets in Base 2

Best Known (111, 111+42, s)-Nets in Base 2

(111, 111+42, 135)-Net over F₂ — Constructive and digital

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+42, 177)-Net over F₂ — Digital

Digital (111, 153, 177)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+42, 1323)-Net in Base 2 — Upper bound on s

There is no (111, 153, 1324)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 11487 665868 929363 145784 592736 897791 675036 871980 > 2¹⁵³ [i]