MinT - Best Known (104−55, 104, s)-Nets in Base 5

Best Known (104−55, 104, s)-Nets in Base 5

(104−55, 104, 82)-Net over F₅ — Constructive and digital

Digital (49, 104, 82)-net over F₅, using

t-expansion [i] based on digital (48, 104, 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]

(104−55, 104, 96)-Net over F₅ — Digital

Digital (49, 104, 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]

(104−55, 104, 1247)-Net in Base 5 — Upper bound on s

There is no (49, 104, 1248)-net in base 5, because

1 times m-reduction [i] would yield (49, 103, 1248)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 998920 120550 828564 230055 719627 891434 370878 746522 397447 620670 323381 321601 > 5¹⁰³ [i]