MinT - Best Known (78, 78+28, s)-Nets in Base 2

Best Known (78, 78+28, s)-Nets in Base 2

(78, 78+28, 102)-Net over F₂ — Constructive and digital

Digital (78, 106, 102)-net over F₂, using

2¹ times duplication [i] based on digital (77, 105, 102)-net over F₂, using
- trace code for nets [i] based on digital (7, 35, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(78, 78+28, 147)-Net over F₂ — Digital

Digital (78, 106, 147)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+28, 1129)-Net in Base 2 — Upper bound on s

There is no (78, 106, 1130)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 81 496589 751991 530711 110170 862064 > 2¹⁰⁶ [i]