MinT - Best Known (48, 48+61, s)-Nets in Base 5

Best Known (48, 48+61, s)-Nets in Base 5

(48, 48+61, 82)-Net over F₅ — Constructive and digital

Digital (48, 109, 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]

(48, 48+61, 92)-Net over F₅ — Digital

Digital (48, 109, 92)-net over F₅, using

t-expansion [i] based on digital (47, 109, 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]

(48, 48+61, 966)-Net in Base 5 — Upper bound on s

There is no (48, 109, 967)-net in base 5, because

1 times m-reduction [i] would yield (48, 108, 967)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3102 724810 892962 894409 115888 397733 618676 234245 544763 358283 743083 906314 967689 > 5¹⁰⁸ [i]