MinT - Best Known (230−102, 230, s)-Nets in Base 2

Best Known (230−102, 230, s)-Nets in Base 2

(230−102, 230, 63)-Net over F₂ — Constructive and digital

Digital (128, 230, 63)-net over F₂, using

4 times m-reduction [i] based on digital (128, 234, 63)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (21, 74, 21)-net over F₂, using
    - net from sequence [i] based on digital (21, 20)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
        an explicitly constructive algebraic function field [i]
  2. digital (54, 160, 42)-net over F₂, using
    - net from sequence [i] based on digital (54, 41)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
        an explicitly constructive algebraic function field [i]

(230−102, 230, 82)-Net over F₂ — Digital

Digital (128, 230, 82)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−102, 230, 297)-Net in Base 2 — Upper bound on s

There is no (128, 230, 298)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2²³⁰, 298, S₂, 102), but
- the linear programming bound shows that MÂ â‰¥ 28328 912148 849580 959168 649431 841394 936395 688011 110123 504172 235246 501853 118396 831712 245536 784384 / 14 303044 917261 608852 030375 > 2²³⁰ [i]