MinT - Best Known (99−39, 99, s)-Nets in Base 5

Best Known (99−39, 99, s)-Nets in Base 5

(99−39, 99, 252)-Net over F₅ — Constructive and digital

Digital (60, 99, 252)-net over F₅, using

1 times m-reduction [i] based on digital (60, 100, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 50, 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]

(99−39, 99, 7972)-Net in Base 5 — Upper bound on s

There is no (60, 99, 7973)-net in base 5, because

1 times m-reduction [i] would yield (60, 98, 7973)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 315 549928 742253 588861 691104 112670 104174 310792 074029 186593 267169 635085 > 5⁹⁸ [i]