MinT - Best Known (49, 49+73, s)-Nets in Base 5

Best Known (49, 49+73, s)-Nets in Base 5

(49, 49+73, 82)-Net over F₅ — Constructive and digital

Digital (49, 122, 82)-net over F₅, using

t-expansion [i] based on digital (48, 122, 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+73, 96)-Net over F₅ — Digital

Digital (49, 122, 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+73, 771)-Net in Base 5 — Upper bound on s

There is no (49, 122, 772)-net in base 5, because

1 times m-reduction [i] would yield (49, 121, 772)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 797233 135313 485227 449021 873000 382421 982064 745444 290122 100101 823217 209133 587198 274305 > 5¹²¹ [i]