MinT - Best Known (150−35, 150, s)-Nets in Base 5

Best Known (150−35, 150, s)-Nets in Base 5

(150−35, 150, 504)-Net over F₅ — Constructive and digital

Digital (115, 150, 504)-net over F₅, using

t-expansion [i] based on digital (113, 150, 504)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (38, 56, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 28, 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]
  2. digital (57, 94, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 47, 126)-net over F₂₅, using
      - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(150−35, 150, 4120)-Net over F₅ — Digital

Digital (115, 150, 4120)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−35, 150, 2399658)-Net in Base 5 — Upper bound on s

There is no (115, 150, 2399659)-net in base 5, because

1 times m-reduction [i] would yield (115, 149, 2399659)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 129979 714593 181681 729331 401532 806777 281075 526605 725438 871357 891083 134144 376463 424106 523440 474207 392365 > 5¹⁴⁹ [i]