MinT - Best Known (59, 59+51, s)-Nets in Base 5

Best Known (59, 59+51, s)-Nets in Base 5

(59, 59+51, 132)-Net over F₅ — Constructive and digital

Digital (59, 110, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 55, 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]

(59, 59+51, 145)-Net over F₅ — Digital

Digital (59, 110, 145)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 59+51, 2820)-Net in Base 5 — Upper bound on s

There is no (59, 110, 2821)-net in base 5, because

1 times m-reduction [i] would yield (59, 109, 2821)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 15516 157744 642731 846409 711870 602603 047949 531627 243020 309662 680350 207972 905013 > 5¹⁰⁹ [i]