MinT - Best Known (46, 46+57, s)-Nets in Base 5

Best Known (46, 46+57, s)-Nets in Base 5

(46, 46+57, 78)-Net over F₅ — Constructive and digital

Digital (46, 103, 78)-net over F₅, using

t-expansion [i] based on digital (38, 103, 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, 46+57, 88)-Net over F₅ — Digital

Digital (46, 103, 88)-net over F₅, using

t-expansion [i] based on digital (45, 103, 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, 46+57, 973)-Net in Base 5 — Upper bound on s

There is no (46, 103, 974)-net in base 5, because

1 times m-reduction [i] would yield (46, 102, 974)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 201668 337125 983076 880453 986035 368724 131286 496040 363827 401596 572605 299393 > 5¹⁰² [i]