MinT - Best Known (82−43, 82, s)-Nets in Base 5

Best Known (82−43, 82, s)-Nets in Base 5

(82−43, 82, 78)-Net over F₅ — Constructive and digital

Digital (39, 82, 78)-net over F₅, using

t-expansion [i] based on digital (38, 82, 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]

(82−43, 82, 1062)-Net in Base 5 — Upper bound on s

There is no (39, 82, 1063)-net in base 5, because

1 times m-reduction [i] would yield (39, 81, 1063)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 418 186981 037301 552881 775483 906920 461355 942472 310664 580685 > 5⁸¹ [i]