MinT - Best Known (37, 37+70, s)-Nets in Base 5

Best Known (37, 37+70, s)-Nets in Base 5

(37, 37+70, 72)-Net over F₅ — Constructive and digital

Digital (37, 107, 72)-net over F₅, using

t-expansion [i] based on digital (31, 107, 72)-net over F₅, using
- net from sequence [i] based on digital (31, 71)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 31 and N(F) ≥ 72, using
    - an explicitly constructive algebraic function field [i]

(37, 37+70, 76)-Net over F₅ — Digital

Digital (37, 107, 76)-net over F₅, using

t-expansion [i] based on digital (34, 107, 76)-net over F₅, using
- net from sequence [i] based on digital (34, 75)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 34 and N(F) ≥ 76, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(37, 37+70, 451)-Net in Base 5 — Upper bound on s

There is no (37, 107, 452)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 652 374178 099765 473352 793635 885120 808154 765543 901746 405260 923925 714763 432465 > 5¹⁰⁷ [i]