MinT - Best Known (119, 119+93, s)-Nets in Base 2

Best Known (119, 119+93, s)-Nets in Base 2

(119, 119+93, 62)-Net over F₂ — Constructive and digital

Digital (119, 212, 62)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (19, 65, 20)-net over F₂, using
  - net from sequence [i] based on digital (19, 19)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, using
      - an explicitly constructive algebraic function field [i]
2. digital (54, 147, 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]

(119, 119+93, 79)-Net over F₂ — Digital

Digital (119, 212, 79)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+93, 298)-Net in Base 2 — Upper bound on s

There is no (119, 212, 299)-net in base 2, because

1 times m-reduction [i] would yield (119, 211, 299)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2²¹¹, 299, S₂, 92), but
  - 1 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]