MinT - Best Known (117, 117+87, s)-Nets in Base 2

Best Known (117, 117+87, s)-Nets in Base 2

(117, 117+87, 66)-Net over F₂ — Constructive and digital

Digital (117, 204, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 102, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(117, 117+87, 81)-Net over F₂ — Digital

Digital (117, 204, 81)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+87, 385)-Net in Base 2 — Upper bound on s

There is no (117, 204, 386)-net in base 2, because

1 times m-reduction [i] would yield (117, 203, 386)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13 951545 819421 623360 966660 763004 612481 140425 312701 931817 670528 > 2²⁰³ [i]