MinT - Best Known (141−101, 141, s)-Nets in Base 5

Best Known (141−101, 141, s)-Nets in Base 5

(141−101, 141, 78)-Net over F₅ — Constructive and digital

Digital (40, 141, 78)-net over F₅, using

t-expansion [i] based on digital (38, 141, 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]

(141−101, 141, 405)-Net in Base 5 — Upper bound on s

There is no (40, 141, 406)-net in base 5, because

1 times m-reduction [i] would yield (40, 140, 406)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 77 300255 343399 700510 869557 761682 816291 595131 730247 621594 129640 523181 486067 920216 397017 507043 842945 > 5¹⁴⁰ [i]