MinT - Best Known (228−67, 228, s)-Nets in Base 2

Best Known (228−67, 228, s)-Nets in Base 2

(228−67, 228, 135)-Net over F₂ — Constructive and digital

Digital (161, 228, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 76, 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]

(228−67, 228, 210)-Net over F₂ — Digital

Digital (161, 228, 210)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(228−67, 228, 1500)-Net in Base 2 — Upper bound on s

There is no (161, 228, 1501)-net in base 2, because

1 times m-reduction [i] would yield (161, 227, 1501)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 216 674756 934900 236392 430170 162703 125077 539764 207856 234691 148575 437652 > 2²²⁷ [i]