MinT - Best Known (105−41, 105, s)-Nets in Base 5

Best Known (105−41, 105, s)-Nets in Base 5

(105−41, 105, 252)-Net over F₅ — Constructive and digital

Digital (64, 105, 252)-net over F₅, using

3 times m-reduction [i] based on digital (64, 108, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 54, 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]

(105−41, 105, 260)-Net over F₅ — Digital

Digital (64, 105, 260)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−41, 105, 8936)-Net in Base 5 — Upper bound on s

There is no (64, 105, 8937)-net in base 5, because

1 times m-reduction [i] would yield (64, 104, 8937)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4 931548 378306 340499 179740 288775 265748 705836 464161 389484 263771 746518 384945 > 5¹⁰⁴ [i]