MinT - Best Known (145−61, 145, s)-Nets in Base 5

Best Known (145−61, 145, s)-Nets in Base 5

(145−61, 145, 252)-Net over F₅ — Constructive and digital

Digital (84, 145, 252)-net over F₅, using

3 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]

(145−61, 145, 259)-Net over F₅ — Digital

Digital (84, 145, 259)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−61, 145, 6798)-Net in Base 5 — Upper bound on s

There is no (84, 145, 6799)-net in base 5, because

1 times m-reduction [i] would yield (84, 144, 6799)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 45033 185839 798679 319315 093820 640125 184773 567090 714714 070933 757590 816781 591948 005493 892446 025704 124809 > 5¹⁴⁴ [i]