MinT - Best Known (98−34, 98, s)-Nets in Base 5

Best Known (98−34, 98, s)-Nets in Base 5

(98−34, 98, 252)-Net over F₅ — Constructive and digital

Digital (64, 98, 252)-net over F₅, using

10 times m-reduction [i] based on digital (64, 108, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 54, 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]

(98−34, 98, 401)-Net over F₅ — Digital

Digital (64, 98, 401)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(98−34, 98, 19185)-Net in Base 5 — Upper bound on s

There is no (64, 98, 19186)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 315 789854 447465 261400 000109 645051 428362 453205 902715 579615 003079 098825 > 5⁹⁸ [i]