MinT - Best Known (115, 115+76, s)-Nets in Base 2

Best Known (115, 115+76, s)-Nets in Base 2

(115, 115+76, 66)-Net over F₂ — Constructive and digital

Digital (115, 191, 66)-net over F₂, using

9 times m-reduction [i] based on 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+76, 90)-Net over F₂ — Digital

Digital (115, 191, 90)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+76, 435)-Net in Base 2 — Upper bound on s

There is no (115, 191, 436)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3152 568993 704128 192842 590617 791000 341794 549307 145178 576356 > 2¹⁹¹ [i]