MinT - Best Known (102−48, 102, s)-Nets in Base 2

Best Known (102−48, 102, s)-Nets in Base 2

(102−48, 102, 42)-Net over F₂ — Constructive and digital

Digital (54, 102, 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]

(102−48, 102, 128)-Net in Base 2 — Upper bound on s

There is no (54, 102, 129)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2¹⁰², 129, S₂, 48), but
- the linear programming bound shows that MÂ â‰¥ 4505 293676 588367 515344 369298 908326 658048 / 781 535645 > 2¹⁰² [i]