MinT - Best Known (50, 50+100, s)-Nets in Base 5

Best Known (50, 50+100, s)-Nets in Base 5

(50, 50+100, 82)-Net over F₅ — Constructive and digital

Digital (50, 150, 82)-net over F₅, using

t-expansion [i] based on digital (48, 150, 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]

(50, 50+100, 96)-Net over F₅ — Digital

Digital (50, 150, 96)-net over F₅, using

t-expansion [i] based on digital (49, 150, 96)-net over F₅, using
- net from sequence [i] based on digital (49, 95)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 49 and N(F) ≥ 96, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(50, 50+100, 572)-Net in Base 5 — Upper bound on s

There is no (50, 150, 573)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 722 404626 729708 473526 942747 935119 666465 848520 280075 501713 053998 412176 767924 441364 055457 941674 637784 782681 > 5¹⁵⁰ [i]