MinT - Best Known (90, 90+54, s)-Nets in Base 5

Best Known (90, 90+54, s)-Nets in Base 5

(90, 90+54, 252)-Net over F₅ — Constructive and digital

Digital (90, 144, 252)-net over F₅, using

t-expansion [i] based on digital (85, 144, 252)-net over F₅, using
- 6 times m-reduction [i] based on digital (85, 150, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 75, 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]

(90, 90+54, 393)-Net over F₅ — Digital

Digital (90, 144, 393)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+54, 14574)-Net in Base 5 — Upper bound on s

There is no (90, 144, 14575)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 44868 246416 703432 785584 630488 543136 893969 672428 485577 375622 127295 971541 296268 624182 450949 518775 351893 > 5¹⁴⁴ [i]