MinT - Best Known (72, 72+48, s)-Nets in Base 5

Best Known (72, 72+48, s)-Nets in Base 5

(72, 72+48, 252)-Net over F₅ — Constructive and digital

Digital (72, 120, 252)-net over F₅, using

4 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+48, 265)-Net over F₅ — Digital

Digital (72, 120, 265)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+48, 7641)-Net in Base 5 — Upper bound on s

There is no (72, 120, 7642)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 754266 215995 642523 551133 817962 335243 530090 294126 348138 222654 455706 267689 554266 666625 > 5¹²⁰ [i]