MinT - Best Known (135, 135+54, s)-Nets in Base 2

Best Known (135, 135+54, s)-Nets in Base 2

(135, 135+54, 135)-Net over F₂ — Constructive and digital

Digital (135, 189, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 63, 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]

(135, 135+54, 191)-Net over F₂ — Digital

Digital (135, 189, 191)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+54, 1358)-Net in Base 2 — Upper bound on s

There is no (135, 189, 1359)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 786 644800 568374 130735 291543 306040 597240 819500 433199 623304 > 2¹⁸⁹ [i]