MinT - Best Known (137−97, 137, s)-Nets in Base 5

Best Known (137−97, 137, s)-Nets in Base 5

(137−97, 137, 78)-Net over F₅ — Constructive and digital

Digital (40, 137, 78)-net over F₅, using

t-expansion [i] based on digital (38, 137, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(137−97, 137, 413)-Net in Base 5 — Upper bound on s

There is no (40, 137, 414)-net in base 5, because

1 times m-reduction [i] would yield (40, 136, 414)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 123401 881752 593433 232108 474203 603611 927564 125703 849581 941914 328660 728433 558162 709735 702825 633025 > 5¹³⁶ [i]