MinT - Best Known (75, 75+38, s)-Nets in Base 5

Best Known (75, 75+38, s)-Nets in Base 5

(75, 75+38, 252)-Net over F₅ — Constructive and digital

Digital (75, 113, 252)-net over F₅, using

17 times m-reduction [i] based on digital (75, 130, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 65, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(75, 75+38, 511)-Net over F₅ — Digital

Digital (75, 113, 511)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+38, 28443)-Net in Base 5 — Upper bound on s

There is no (75, 113, 28444)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 9 635076 184700 568788 826132 738246 739978 260367 056448 047118 130055 414171 457344 031345 > 5¹¹³ [i]