MinT - Best Known (46, 123, s)-Nets in Base 5

Best Known (46, 123, s)-Nets in Base 5

(46, 123, 78)-Net over F₅ — Constructive and digital

Digital (46, 123, 78)-net over F₅, using

t-expansion [i] based on digital (38, 123, 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]

(46, 123, 88)-Net over F₅ — Digital

Digital (46, 123, 88)-net over F₅, using

t-expansion [i] based on digital (45, 123, 88)-net over F₅, using
- net from sequence [i] based on digital (45, 87)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 45 and N(F) ≥ 88, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(46, 123, 631)-Net in Base 5 — Upper bound on s

There is no (46, 123, 632)-net in base 5, because

1 times m-reduction [i] would yield (46, 122, 632)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 19 590093 950950 481178 255093 679265 089074 510178 813483 913751 595870 245639 954103 562843 210625 > 5¹²² [i]