MinT - Best Known (145−71, 145, s)-Nets in Base 5

Best Known (145−71, 145, s)-Nets in Base 5

(145−71, 145, 95)-Net over F₅ — Constructive and digital

Digital (74, 145, 95)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (8, 43, 23)-net over F₅, using
  - net from sequence [i] based on digital (8, 22)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₅ with g(F)Â =Â 7, N(F)Â =Â 22, and 1 place with degree 2 [i] based on function field F/F₅ with g(F) = 7 and N(F) ≥ 22, using an explicitly constructive algebraic function field [i]
2. digital (31, 102, 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]

(145−71, 145, 152)-Net over F₅ — Digital

Digital (74, 145, 152)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−71, 145, 2586)-Net in Base 5 — Upper bound on s

There is no (74, 145, 2587)-net in base 5, because

1 times m-reduction [i] would yield (74, 144, 2587)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 45265 466853 166547 185730 767825 915614 520381 468649 419555 083589 014396 779453 527086 877466 109745 885606 293797 > 5¹⁴⁴ [i]