MinT - Best Known (203−149, 203, s)-Nets in Base 2

Best Known (203−149, 203, s)-Nets in Base 2

(203−149, 203, 42)-Net over F₂ — Constructive and digital

Digital (54, 203, 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]

(203−149, 203, 69)-Net in Base 2 — Upper bound on s

There is no (54, 203, 70)-net in base 2, because

extracting embedded OOA [i] would yield OOA(2²⁰³, 70, S₂, 3, 149), but
- the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 205 688069 665150 755269 371147 819668 813122 841983 204197 482918 576128 / 15 > 2²⁰³ [i]