MinT - Best Known (143−95, 143, s)-Nets in Base 5

Best Known (143−95, 143, s)-Nets in Base 5

(143−95, 143, 82)-Net over F₅ — Constructive and digital

Digital (48, 143, 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]

(143−95, 143, 92)-Net over F₅ — Digital

Digital (48, 143, 92)-net over F₅, using

t-expansion [i] based on digital (47, 143, 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]

(143−95, 143, 560)-Net in Base 5 — Upper bound on s

There is no (48, 143, 561)-net in base 5, because

1 times m-reduction [i] would yield (48, 142, 561)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1941 322545 244812 864028 165900 201947 474734 981223 222184 625500 418645 429218 550986 630491 331735 864401 208525 > 5¹⁴² [i]