MinT - Best Known (83, 83+63, s)-Nets in Base 2

Best Known (83, 83+63, s)-Nets in Base 2

(83, 83+63, 54)-Net over F₂ — Constructive and digital

Digital (83, 146, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 73, 27)-net over F₄, using
- net from sequence [i] based on digital (10, 26)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]

(83, 83+63, 60)-Net over F₂ — Digital

Digital (83, 146, 60)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+63, 274)-Net in Base 2 — Upper bound on s

There is no (83, 146, 275)-net in base 2, because

1 times m-reduction [i] would yield (83, 145, 275)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 46 562597 718409 962036 821482 760489 167017 263232 > 2¹⁴⁵ [i]