MinT - Best Known (110−56, 110, s)-Nets in Base 5

Best Known (110−56, 110, s)-Nets in Base 5

(110−56, 110, 82)-Net over F₅ — Constructive and digital

Digital (54, 110, 82)-net over F₅, using

t-expansion [i] based on digital (48, 110, 82)-net over F₅, using
- net from sequence [i] based on digital (48, 81)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
    - an explicitly constructive algebraic function field [i]

(110−56, 110, 106)-Net over F₅ — Digital

Digital (54, 110, 106)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(110−56, 110, 1553)-Net in Base 5 — Upper bound on s

There is no (54, 110, 1554)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 78126 569739 387264 350796 986848 480969 606670 618216 935899 692209 990761 310085 646017 > 5¹¹⁰ [i]