MinT - Best Known (79, 79+61, s)-Nets in Base 5

Best Known (79, 79+61, s)-Nets in Base 5

(79, 79+61, 208)-Net over F₅ — Constructive and digital

Digital (79, 140, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 70, 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]

(79, 79+61, 221)-Net over F₅ — Digital

Digital (79, 140, 221)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+61, 5193)-Net in Base 5 — Upper bound on s

There is no (79, 140, 5194)-net in base 5, because

1 times m-reduction [i] would yield (79, 139, 5194)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 14 394092 305964 622904 042054 946273 761999 746275 597292 632276 526847 740170 947015 954859 084672 420970 044161 > 5¹³⁹ [i]