MinT - Best Known (114, 114+76, s)-Nets in Base 2

Best Known (114, 114+76, s)-Nets in Base 2

(114, 114+76, 66)-Net over F₂ — Constructive and digital

Digital (114, 190, 66)-net over F₂, using

8 times m-reduction [i] based on digital (114, 198, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 99, 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]

(114, 114+76, 88)-Net over F₂ — Digital

Digital (114, 190, 88)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 114+76, 427)-Net in Base 2 — Upper bound on s

There is no (114, 190, 428)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1680 058877 266667 826534 984634 733282 375266 703156 096882 973838 > 2¹⁹⁰ [i]