MinT - Best Known (84−41, 84, s)-Nets in Base 5

Best Known (84−41, 84, s)-Nets in Base 5

(84−41, 84, 78)-Net over F₅ — Constructive and digital

Digital (43, 84, 78)-net over F₅, using

t-expansion [i] based on digital (38, 84, 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]

(84−41, 84, 98)-Net over F₅ — Digital

Digital (43, 84, 98)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−41, 84, 1637)-Net in Base 5 — Upper bound on s

There is no (43, 84, 1638)-net in base 5, because

1 times m-reduction [i] would yield (43, 83, 1638)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 10415 109623 670671 877379 466426 974994 741181 734571 726278 857025 > 5⁸³ [i]