MinT - Best Known (234−102, 234, s)-Nets in Base 2

Best Known (234−102, 234, s)-Nets in Base 2

(234−102, 234, 66)-Net over F₂ — Constructive and digital

Digital (132, 234, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 117, 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]

(234−102, 234, 87)-Net over F₂ — Digital

Digital (132, 234, 87)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−102, 234, 406)-Net in Base 2 — Upper bound on s

There is no (132, 234, 407)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 28574 167643 528083 340189 310908 149022 368009 164510 873638 485774 287379 460744 > 2²³⁴ [i]