MinT - Best Known (103, 176, s)-Nets in Base 2

Best Known (103, 176, s)-Nets in Base 2

(103, 176, 66)-Net over F₂ — Constructive and digital

Digital (103, 176, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 88, 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]

(103, 176, 76)-Net over F₂ — Digital

Digital (103, 176, 76)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(103, 176, 364)-Net in Base 2 — Upper bound on s

There is no (103, 176, 365)-net in base 2, because

1 times m-reduction [i] would yield (103, 175, 365)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 50142 324809 601159 049676 717483 335376 336722 211821 864053 > 2¹⁷⁵ [i]