MinT - Best Known (101−53, 101, s)-Nets in Base 5

Best Known (101−53, 101, s)-Nets in Base 5

(101−53, 101, 82)-Net over F₅ — Constructive and digital

Digital (48, 101, 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]

(101−53, 101, 92)-Net over F₅ — Digital

Digital (48, 101, 92)-net over F₅, using

t-expansion [i] based on digital (47, 101, 92)-net over F₅, using
- net from sequence [i] based on digital (47, 91)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 47 and N(F) ≥ 92, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(101−53, 101, 1268)-Net in Base 5 — Upper bound on s

There is no (48, 101, 1269)-net in base 5, because

1 times m-reduction [i] would yield (48, 100, 1269)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 8032 980600 703371 798427 243062 275931 400053 054778 916028 122484 190786 020025 > 5¹⁰⁰ [i]