MinT - Best Known (104, 104+41, s)-Nets in Base 2

Best Known (104, 104+41, s)-Nets in Base 2

(104, 104+41, 102)-Net over F₂ — Constructive and digital

Digital (104, 145, 102)-net over F₂, using

2¹ times duplication [i] based on digital (103, 144, 102)-net over F₂, using
- trace code for nets [i] based on digital (7, 48, 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]

(104, 104+41, 158)-Net over F₂ — Digital

Digital (104, 145, 158)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(104, 104+41, 1191)-Net in Base 2 — Upper bound on s

There is no (104, 145, 1192)-net in base 2, because

1 times m-reduction [i] would yield (104, 144, 1192)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 22 359745 833342 038285 107476 926604 311036 993122 > 2¹⁴⁴ [i]