MinT - Best Known (30−21, 30, s)-Nets in Base 5

Best Known (30−21, 30, s)-Nets in Base 5

(30−21, 30, 26)-Net over F₅ — Constructive and digital

Digital (9, 30, 26)-net over F₅, using

net from sequence [i] based on digital (9, 25)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 9 and N(F) ≥ 26, using
  - an explicitly constructive algebraic function field [i]

(30−21, 30, 113)-Net in Base 5 — Upper bound on s

There is no (9, 30, 114)-net in base 5, because

1 times m-reduction [i] would yield (9, 29, 114)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 192 051638 142564 552641 > 5²⁹ [i]