MinT - Best Known (58, 58+37, s)-Nets in Base 5

Best Known (58, 58+37, s)-Nets in Base 5

(58, 58+37, 252)-Net over F₅ — Constructive and digital

Digital (58, 95, 252)-net over F₅, using

1 times m-reduction [i] based on digital (58, 96, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 48, 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]

(58, 58+37, 8425)-Net in Base 5 — Upper bound on s

There is no (58, 95, 8426)-net in base 5, because

1 times m-reduction [i] would yield (58, 94, 8426)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 505789 567146 794730 731354 062438 853880 307495 607331 516678 284928 825025 > 5⁹⁴ [i]