MinT - Best Known (210−92, 210, s)-Nets in Base 2

Best Known (210−92, 210, s)-Nets in Base 2

(210−92, 210, 60)-Net over F₂ — Constructive and digital

Digital (118, 210, 60)-net over F₂, using

trace code for nets [i] based on digital (13, 105, 30)-net over F₄, using
- net from sequence [i] based on digital (13, 29)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
    - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(210−92, 210, 78)-Net over F₂ — Digital

Digital (118, 210, 78)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−92, 210, 297)-Net in Base 2 — Upper bound on s

There is no (118, 210, 298)-net in base 2, because

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]