MinT - Best Known (137−115, 137, s)-Nets in Base 5

Best Known (137−115, 137, s)-Nets in Base 5

(137−115, 137, 51)-Net over F₅ — Constructive and digital

Digital (22, 137, 51)-net over F₅, using

net from sequence [i] based on digital (22, 50)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
  - an explicitly constructive algebraic function field [i]

(137−115, 137, 115)-Net in Base 5 — Upper bound on s

There is no (22, 137, 116)-net in base 5, because

34 times m-reduction [i] would yield (22, 103, 116)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5¹⁰³, 116, S₅, 81), but
  - the linear programming bound shows that MÂ â‰¥ 1237 818286 417009 129589 313695 434643 806752 260386 527808 577739 051543 176174 163818 359375 / 1092 587229 > 5¹⁰³ [i]