MinT - Best Known (49, 49+97, s)-Nets in Base 5

Best Known (49, 49+97, s)-Nets in Base 5

(49, 49+97, 82)-Net over F₅ — Constructive and digital

Digital (49, 146, 82)-net over F₅, using

t-expansion [i] based on digital (48, 146, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(49, 49+97, 96)-Net over F₅ — Digital

Digital (49, 146, 96)-net over F₅, using

net from sequence [i] based on digital (49, 95)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 49 and N(F) ≥ 96, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(49, 49+97, 570)-Net in Base 5 — Upper bound on s

There is no (49, 146, 571)-net in base 5, because

1 times m-reduction [i] would yield (49, 145, 571)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 227044 015379 202270 476769 936983 708312 035835 161345 537827 496788 147826 581897 736853 725271 547483 170261 244225 > 5¹⁴⁵ [i]