MinT - Best Known (122−47, 122, s)-Nets in Base 5

Best Known (122−47, 122, s)-Nets in Base 5

(122−47, 122, 252)-Net over F₅ — Constructive and digital

Digital (75, 122, 252)-net over F₅, using

8 times m-reduction [i] based on digital (75, 130, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 65, 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]

(122−47, 122, 309)-Net over F₅ — Digital

Digital (75, 122, 309)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(122−47, 122, 11192)-Net in Base 5 — Upper bound on s

There is no (75, 122, 11193)-net in base 5, because

1 times m-reduction [i] would yield (75, 121, 11193)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 763428 476814 186803 680125 183127 162021 156553 888306 767844 246101 353055 920630 263691 298125 > 5¹²¹ [i]