MinT - Best Known (53, 108, s)-Nets in Base 5

Best Known (53, 108, s)-Nets in Base 5

(53, 108, 82)-Net over F₅ — Constructive and digital

Digital (53, 108, 82)-net over F₅, using

t-expansion [i] based on digital (48, 108, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(53, 108, 104)-Net over F₅ — Digital

Digital (53, 108, 104)-net over F₅, using

t-expansion [i] based on digital (51, 108, 104)-net over F₅, using
- net from sequence [i] based on digital (51, 103)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 51 and N(F) ≥ 104, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(53, 108, 1588)-Net in Base 5 — Upper bound on s

There is no (53, 108, 1589)-net in base 5, because

1 times m-reduction [i] would yield (53, 107, 1589)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 621 151388 028122 434069 966172 106531 223603 970298 890208 365166 760127 779027 583661 > 5¹⁰⁷ [i]