MinT - Best Known (46, 46+100, s)-Nets in Base 5

Best Known (46, 46+100, s)-Nets in Base 5

(46, 46+100, 78)-Net over F₅ — Constructive and digital

Digital (46, 146, 78)-net over F₅, using

t-expansion [i] based on digital (38, 146, 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+100, 88)-Net over F₅ — Digital

Digital (46, 146, 88)-net over F₅, using

t-expansion [i] based on digital (45, 146, 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+100, 499)-Net in Base 5 — Upper bound on s

There is no (46, 146, 500)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 210869 602896 328286 858634 701456 476868 074393 399432 325890 080823 943900 370008 886858 027972 046288 105014 953921 > 5¹⁴⁶ [i]