MinT - Best Known (99−33, 99, s)-Nets in Base 5

Best Known (99−33, 99, s)-Nets in Base 5

(99−33, 99, 252)-Net over F₅ — Constructive and digital

Digital (66, 99, 252)-net over F₅, using

13 times m-reduction [i] based on digital (66, 112, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 56, 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]

(99−33, 99, 481)-Net over F₅ — Digital

Digital (66, 99, 481)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−33, 99, 32472)-Net in Base 5 — Upper bound on s

There is no (66, 99, 32473)-net in base 5, because

1 times m-reduction [i] would yield (66, 98, 32473)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 315 615944 300802 627839 197716 997852 319021 740192 687293 782838 500592 106433 > 5⁹⁸ [i]