MinT - Best Known (30−15, 30, s)-Nets in Base 5

Best Known (30−15, 30, s)-Nets in Base 5

(30−15, 30, 52)-Net over F₅ — Constructive and digital

Digital (15, 30, 52)-net over F₅, using

trace code for nets [i] based on digital (0, 15, 26)-net over F₂₅, using
- net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
    - the rational function field F₂₅(x) [i]
  - Niederreiter sequence [i]

(30−15, 30, 659)-Net in Base 5 — Upper bound on s

There is no (15, 30, 660)-net in base 5, because

1 times m-reduction [i] would yield (15, 29, 660)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 186 439996 109218 400209 > 5²⁹ [i]