MinT - Best Known (67, 67+43, s)-Nets in Base 5

Best Known (67, 67+43, s)-Nets in Base 5

(67, 67+43, 252)-Net over F₅ — Constructive and digital

Digital (67, 110, 252)-net over F₅, using

4 times m-reduction [i] based on digital (67, 114, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 57, 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]

(67, 67+43, 269)-Net over F₅ — Digital

Digital (67, 110, 269)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+43, 9198)-Net in Base 5 — Upper bound on s

There is no (67, 110, 9199)-net in base 5, because

1 times m-reduction [i] would yield (67, 109, 9199)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 15437 135356 366903 802172 871971 541637 507747 862934 764525 688319 417334 904764 836717 > 5¹⁰⁹ [i]