MinT - Best Known (63−33, 63, s)-Nets in Base 5

Best Known (63−33, 63, s)-Nets in Base 5

(63−33, 63, 51)-Net over F₅ — Constructive and digital

Digital (30, 63, 51)-net over F₅, using

t-expansion [i] based on digital (22, 63, 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]

(63−33, 63, 62)-Net over F₅ — Digital

Digital (30, 63, 62)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(63−33, 63, 857)-Net in Base 5 — Upper bound on s

There is no (30, 63, 858)-net in base 5, because

1 times m-reduction [i] would yield (30, 62, 858)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 21 888400 741786 116945 534093 405136 776648 893185 > 5⁶² [i]