MinT - Best Known (138−54, 138, s)-Nets in Base 5

Best Known (138−54, 138, s)-Nets in Base 5

(138−54, 138, 252)-Net over F₅ — Constructive and digital

Digital (84, 138, 252)-net over F₅, using

10 times m-reduction [i] based on digital (84, 148, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 74, 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]

(138−54, 138, 323)-Net over F₅ — Digital

Digital (84, 138, 323)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(138−54, 138, 10186)-Net in Base 5 — Upper bound on s

There is no (84, 138, 10187)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 874637 728620 716773 533439 353652 535510 334904 555068 352159 543723 490310 578406 671746 795767 621715 418885 > 5¹³⁸ [i]