MinT - Best Known (232−101, 232, s)-Nets in Base 2

Best Known (232−101, 232, s)-Nets in Base 2

(232−101, 232, 66)-Net over F₂ — Constructive and digital

Digital (131, 232, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 116, 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]

(232−101, 232, 86)-Net over F₂ — Digital

Digital (131, 232, 86)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−101, 232, 409)-Net in Base 2 — Upper bound on s

There is no (131, 232, 410)-net in base 2, because

1 times m-reduction [i] would yield (131, 231, 410)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3644 582511 257619 840549 715841 895003 352900 306995 194403 734463 660954 371568 > 2²³¹ [i]