MinT - Best Known (72, 72+46, s)-Nets in Base 5

Best Known (72, 72+46, s)-Nets in Base 5

(72, 72+46, 252)-Net over F₅ — Constructive and digital

Digital (72, 118, 252)-net over F₅, using

6 times m-reduction [i] based on digital (72, 124, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 62, 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]

(72, 72+46, 287)-Net over F₅ — Digital

Digital (72, 118, 287)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+46, 9070)-Net in Base 5 — Upper bound on s

There is no (72, 118, 9071)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 30155 719796 427511 169955 104579 164167 447170 932145 097709 127994 652527 394928 935692 647525 > 5¹¹⁸ [i]