MinT - Best Known (115, 115+85, s)-Nets in Base 2

Best Known (115, 115+85, s)-Nets in Base 2

(115, 115+85, 66)-Net over F₂ — Constructive and digital

Digital (115, 200, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 100, 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]

(115, 115+85, 80)-Net over F₂ — Digital

Digital (115, 200, 80)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+85, 381)-Net in Base 2 — Upper bound on s

There is no (115, 200, 382)-net in base 2, because

1 times m-reduction [i] would yield (115, 199, 382)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 808821 884497 988922 674990 260453 954466 180779 554719 700904 266370 > 2¹⁹⁹ [i]