MinT - Best Known (47, 47+91, s)-Nets in Base 5

Best Known (47, 47+91, s)-Nets in Base 5

(47, 47+91, 78)-Net over F₅ — Constructive and digital

Digital (47, 138, 78)-net over F₅, using

t-expansion [i] based on digital (38, 138, 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, 47+91, 92)-Net over F₅ — Digital

Digital (47, 138, 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, 47+91, 559)-Net in Base 5 — Upper bound on s

There is no (47, 138, 560)-net in base 5, because

1 times m-reduction [i] would yield (47, 137, 560)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 615576 103317 092440 162823 376246 414636 111097 665492 762535 233753 451952 725575 479627 838681 388600 484545 > 5¹³⁷ [i]