MinT - Best Known (68, 103, s)-Nets in Base 5

Best Known (68, 103, s)-Nets in Base 5

(68, 103, 252)-Net over F₅ — Constructive and digital

Digital (68, 103, 252)-net over F₅, using

13 times m-reduction [i] based on digital (68, 116, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 58, 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]

(68, 103, 456)-Net over F₅ — Digital

Digital (68, 103, 456)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 103, 28023)-Net in Base 5 — Upper bound on s

There is no (68, 103, 28024)-net in base 5, because

1 times m-reduction [i] would yield (68, 102, 28024)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 197328 371905 916291 163697 914786 345885 781364 256585 475951 502002 564484 954593 > 5¹⁰² [i]