MinT - Best Known (156−43, 156, s)-Nets in Base 2

Best Known (156−43, 156, s)-Nets in Base 2

(156−43, 156, 135)-Net over F₂ — Constructive and digital

Digital (113, 156, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 52, 45)-net over F₈, using
- net from sequence [i] based on digital (9, 44)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
    - an explicitly constructive algebraic function field [i]

(156−43, 156, 178)-Net over F₂ — Digital

Digital (113, 156, 178)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(156−43, 156, 1416)-Net in Base 2 — Upper bound on s

There is no (113, 156, 1417)-net in base 2, because

1 times m-reduction [i] would yield (113, 155, 1417)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 46335 317253 335280 082898 745374 496087 058086 866976 > 2¹⁵⁵ [i]