MinT - Best Known (118, 118+93, s)-Nets in Base 2

Best Known (118, 118+93, s)-Nets in Base 2

(118, 118+93, 59)-Net over F₂ — Constructive and digital

Digital (118, 211, 59)-net over F₂, using

5 times m-reduction [i] based on digital (118, 216, 59)-net over F₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (15, 64, 17)-net over F₂, using
    - net from sequence [i] based on digital (15, 16)-sequence over F₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, using
        an explicitly constructive algebraic function field [i]
  2. digital (54, 152, 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]

(118, 118+93, 77)-Net over F₂ — Digital

Digital (118, 211, 77)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 118+93, 297)-Net in Base 2 — Upper bound on s

There is no (118, 211, 298)-net in base 2, because

1 times m-reduction [i] would yield (118, 210, 298)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2²¹⁰, 298, S₂, 92), but
  - 2 times code embedding in larger space [i] would yield OA(2²¹², 300, S₂, 92), but
    - the linear programming bound shows that MÂ â‰¥ 2484 132694 351399 471861 447697 940992 402712 231248 004226 234322 576635 442083 069406 167011 327832 607273 517056 / 377277 818302 855799 777736 052112 623275 > 2²¹² [i]