MinT - Best Known (15, 15+134, s)-Nets in Base 5

Best Known (15, 15+134, s)-Nets in Base 5

(15, 15+134, 36)-Net over F₅ — Constructive and digital

Digital (15, 149, 36)-net over F₅, using

net from sequence [i] based on digital (15, 35)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₅ with g(F)Â =Â 11, N(F)Â =Â 32, and 4 places with degree 2 [i] based on function field F/F₅ with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]

(15, 15+134, 39)-Net over F₅ — Digital

Digital (15, 149, 39)-net over F₅, using

t-expansion [i] based on digital (14, 149, 39)-net over F₅, using
- net from sequence [i] based on digital (14, 38)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 14 and N(F) ≥ 39, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(15, 15+134, 75)-Net in Base 5 — Upper bound on s

There is no (15, 149, 76)-net in base 5, because

1 times m-reduction [i] would yield (15, 148, 76)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5¹⁴⁸, 76, S₅, 2, 133), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 2101 947696 487225 606385 594374 934874 196920 392912 814773 657635 602425 834686 624028 790902 229957 282543 182373 046875 / 67 > 5¹⁴⁸ [i]