MinT - Best Known (58, 58+33, s)-Nets in Base 5

Best Known (58, 58+33, s)-Nets in Base 5

(58, 58+33, 252)-Net over F₅ — Constructive and digital

Digital (58, 91, 252)-net over F₅, using

5 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+33, 314)-Net over F₅ — Digital

Digital (58, 91, 314)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+33, 14515)-Net in Base 5 — Upper bound on s

There is no (58, 91, 14516)-net in base 5, because

1 times m-reduction [i] would yield (58, 90, 14516)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 807 965523 193687 563436 874627 186035 446413 469373 362274 686900 076545 > 5⁹⁰ [i]