MinT - Best Known (137−126, 137, s)-Nets in Base 5

Best Known (137−126, 137, s)-Nets in Base 5

(137−126, 137, 32)-Net over F₅ — Constructive and digital

Digital (11, 137, 32)-net over F₅, using

net from sequence [i] based on digital (11, 31)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 11 and N(F) ≥ 32, using
  - an explicitly constructive algebraic function field [i]

(137−126, 137, 57)-Net in Base 5 — Upper bound on s

There is no (11, 137, 58)-net in base 5, because

24 times m-reduction [i] would yield (11, 113, 58)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5¹¹³, 58, S₅, 2, 102), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 1107 409718 022660 615507 187316 986333 208159 408447 723848 212262 964807 450771 331787 109375 / 103 > 5¹¹³ [i]