MinT - Best Known (214−94, 214, s)-Nets in Base 2

Best Known (214−94, 214, s)-Nets in Base 2

(214−94, 214, 62)-Net over F₂ — Constructive and digital

Digital (120, 214, 62)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (19, 66, 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, 148, 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]

(214−94, 214, 79)-Net over F₂ — Digital

Digital (120, 214, 79)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−94, 214, 297)-Net in Base 2 — Upper bound on s

There is no (120, 214, 298)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2²¹⁴, 298, S₂, 94), but
- 1 times code embedding in larger space [i] would yield OA(2²¹⁵, 299, S₂, 94), but
  - adding a parity check bit [i] would yield OA(2²¹⁶, 300, S₂, 95), but
    - the linear programming bound shows that MÂ â‰¥ 872407 680551 113098 866799 953294 886066 311827 924058 628412 428016 149220 115296 187426 023936 653562 740736 / 5 938078 052347 021578 779474 608305 > 2²¹⁶ [i]