MinT - Best Known (30, 30+31, s)-Nets in Base 5

Best Known (30, 30+31, s)-Nets in Base 5

(30, 30+31, 51)-Net over F₅ — Constructive and digital

Digital (30, 61, 51)-net over F₅, using

t-expansion [i] based on digital (22, 61, 51)-net over F₅, using
- net from sequence [i] based on digital (22, 50)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
    - an explicitly constructive algebraic function field [i]

(30, 30+31, 68)-Net over F₅ — Digital

Digital (30, 61, 68)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(30, 30+31, 992)-Net in Base 5 — Upper bound on s

There is no (30, 61, 993)-net in base 5, because

1 times m-reduction [i] would yield (30, 60, 993)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 867985 498935 495261 860156 509637 455482 790669 > 5⁶⁰ [i]