MinT - Best Known (47, 47+85, s)-Nets in Base 5

Best Known (47, 47+85, s)-Nets in Base 5

(47, 47+85, 78)-Net over F₅ — Constructive and digital

Digital (47, 132, 78)-net over F₅, using

t-expansion [i] based on digital (38, 132, 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+85, 92)-Net over F₅ — Digital

Digital (47, 132, 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+85, 594)-Net in Base 5 — Upper bound on s

There is no (47, 132, 595)-net in base 5, because

1 times m-reduction [i] would yield (47, 131, 595)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 37 964992 913280 963611 561462 940362 360531 325595 436425 091544 187869 821320 114144 090783 180419 524313 > 5¹³¹ [i]