MinT - Best Known (114, 114+31, s)-Nets in Base 2

Best Known (114, 114+31, s)-Nets in Base 2

(114, 114+31, 196)-Net over F₂ — Constructive and digital

Digital (114, 145, 196)-net over F₂, using

2¹ times duplication [i] based on digital (113, 144, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 36, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(114, 114+31, 330)-Net over F₂ — Digital

Digital (114, 145, 330)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 114+31, 4962)-Net in Base 2 — Upper bound on s

There is no (114, 145, 4963)-net in base 2, because

1 times m-reduction [i] would yield (114, 144, 4963)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 22 305937 098899 241697 974030 394283 427672 361808 > 2¹⁴⁴ [i]