MinT - Best Known (58, 58+30, s)-Nets in Base 5

Best Known (58, 58+30, s)-Nets in Base 5

(58, 58+30, 252)-Net over F₅ — Constructive and digital

Digital (58, 88, 252)-net over F₅, using

8 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+30, 400)-Net over F₅ — Digital

Digital (58, 88, 400)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+30, 20234)-Net in Base 5 — Upper bound on s

There is no (58, 88, 20235)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 32 315258 589432 359151 367642 653765 936361 024555 209588 541037 147445 > 5⁸⁸ [i]