MinT - Best Known (72, 72+26, s)-Nets in Base 5

Best Known (72, 72+26, s)-Nets in Base 5

(72, 72+26, 304)-Net over F₅ — Constructive and digital

Digital (72, 98, 304)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (13, 26, 52)-net over F₅, using
  - trace code for nets [i] based on digital (0, 13, 26)-net over F₂₅, using
    - net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
        the rational function field F₂₅(x) [i]
      - Niederreiter sequence [i]
2. digital (46, 72, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 36, 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+26, 1410)-Net over F₅ — Digital

Digital (72, 98, 1410)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+26, 263323)-Net in Base 5 — Upper bound on s

There is no (72, 98, 263324)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 315 553976 291946 742445 162097 359162 764449 545182 353962 810490 437781 633009 > 5⁹⁸ [i]