MinT - Best Known (188−79, 188, s)-Nets in Base 2

Best Known (188−79, 188, s)-Nets in Base 2

(188−79, 188, 66)-Net over F₂ — Constructive and digital

Digital (109, 188, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 94, 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]

(188−79, 188, 78)-Net over F₂ — Digital

Digital (109, 188, 78)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−79, 188, 372)-Net in Base 2 — Upper bound on s

There is no (109, 188, 373)-net in base 2, because

1 times m-reduction [i] would yield (109, 187, 373)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 200 857335 463505 248115 356842 868478 092920 088807 934234 536824 > 2¹⁸⁷ [i]