MinT - Best Known (47, 144, s)-Nets in Base 5

Best Known (47, 144, s)-Nets in Base 5

(47, 144, 78)-Net over F₅ — Constructive and digital

Digital (47, 144, 78)-net over F₅, using

t-expansion [i] based on digital (38, 144, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(47, 144, 92)-Net over F₅ — Digital

Digital (47, 144, 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]

(47, 144, 531)-Net in Base 5 — Upper bound on s

There is no (47, 144, 532)-net in base 5, because

1 times m-reduction [i] would yield (47, 143, 532)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9270 911044 344729 624205 063834 549859 355268 180071 307125 568392 939265 577118 687344 762989 134595 301373 722625 > 5¹⁴³ [i]