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

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

(61, 61+61, 82)-Net over F₅ — Constructive and digital

Digital (61, 122, 82)-net over F₅, using

t-expansion [i] based on digital (48, 122, 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]

(61, 61+61, 122)-Net over F₅ — Digital

Digital (61, 122, 122)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(61, 61+61, 1963)-Net in Base 5 — Upper bound on s

There is no (61, 122, 1964)-net in base 5, because

1 times m-reduction [i] would yield (61, 121, 1964)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3 775263 845052 366817 455726 939698 082838 013844 922226 204076 105118 919612 601808 212242 652481 > 5¹²¹ [i]