MinT - Best Known (72−67, 72, s)-Nets in Base 25

Best Known (72−67, 72, s)-Nets in Base 25

(72−67, 72, 66)-Net over F₂₅ — Constructive and digital

Digital (5, 72, 66)-net over F₂₅, using

t-expansion [i] based on digital (4, 72, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(72−67, 72, 471)-Net in Base 25 — Upper bound on s

There is no (5, 72, 472)-net in base 25, because

29 times m-reduction [i] would yield (5, 43, 472)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1 295541 986408 243846 186651 329441 022761 262698 343113 069611 401665 > 25⁴³ [i]