MinT - Best Known (125−87, 125, s)-Nets in Base 5

Best Known (125−87, 125, s)-Nets in Base 5

(125−87, 125, 78)-Net over F₅ — Constructive and digital

Digital (38, 125, 78)-net over F₅, using

net from sequence [i] based on digital (38, 77)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
  - an explicitly constructive algebraic function field [i]

(125−87, 125, 406)-Net in Base 5 — Upper bound on s

There is no (38, 125, 407)-net in base 5, because

1 times m-reduction [i] would yield (38, 124, 407)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 488 691076 753885 261944 319907 097103 027447 264846 263715 605122 412763 216207 828626 958444 195125 > 5¹²⁴ [i]