MinT - Best Known (115−41, 115, s)-Nets in Base 5

Best Known (115−41, 115, s)-Nets in Base 5

(115−41, 115, 252)-Net over F₅ — Constructive and digital

Digital (74, 115, 252)-net over F₅, using

13 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]

(115−41, 115, 402)-Net over F₅ — Digital

Digital (74, 115, 402)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−41, 115, 20001)-Net in Base 5 — Upper bound on s

There is no (74, 115, 20002)-net in base 5, because

1 times m-reduction [i] would yield (74, 114, 20002)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 48 176625 915137 872955 617657 180346 005163 097624 633734 298529 813962 358545 508036 194625 > 5¹¹⁴ [i]