MinT - Best Known (64−23, 64, s)-Nets in Base 5

Best Known (64−23, 64, s)-Nets in Base 5

(64−23, 64, 208)-Net over F₅ — Constructive and digital

Digital (41, 64, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 32, 104)-net over F₂₅, using
- net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
    - a function field by GarcÃa and Quoos [i]

(64−23, 64, 255)-Net over F₅ — Digital

Digital (41, 64, 255)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(64−23, 64, 12355)-Net in Base 5 — Upper bound on s

There is no (41, 64, 12356)-net in base 5, because

1 times m-reduction [i] would yield (41, 63, 12356)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 108 431597 688622 424600 835292 420411 839576 126225 > 5⁶³ [i]