MinT - Best Known (123−49, 123, s)-Nets in Base 5

Best Known (123−49, 123, s)-Nets in Base 5

(123−49, 123, 252)-Net over F₅ — Constructive and digital

Digital (74, 123, 252)-net over F₅, using

5 times m-reduction [i] based on digital (74, 128, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 64, 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]

(123−49, 123, 274)-Net over F₅ — Digital

Digital (74, 123, 274)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(123−49, 123, 8740)-Net in Base 5 — Upper bound on s

There is no (74, 123, 8741)-net in base 5, because

1 times m-reduction [i] would yield (74, 122, 8741)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 18 837912 932920 138776 177266 047978 491102 785562 676087 821946 532613 861389 671394 923851 544225 > 5¹²² [i]