MinT - Best Known (257−203, 257, s)-Nets in Base 2

Best Known (257−203, 257, s)-Nets in Base 2

(257−203, 257, 42)-Net over F₂ — Constructive and digital

Digital (54, 257, 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]

(257−203, 257, 65)-Net in Base 2 — Upper bound on s

There is no (54, 257, 66)-net in base 2, because

1 times m-reduction [i] would yield (54, 256, 66)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2²⁵⁶, 66, S₂, 4, 202), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 3 705346 855594 118253 554271 520278 013051 304639 509300 498049 262642 688253 220148 477952 / 29 > 2²⁵⁶ [i]