MinT - Best Known (53, 53+45, s)-Nets in Base 5

Best Known (53, 53+45, s)-Nets in Base 5

(53, 53+45, 132)-Net over F₅ — Constructive and digital

Digital (53, 98, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 49, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(53, 53+45, 137)-Net over F₅ — Digital

Digital (53, 98, 137)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+45, 2716)-Net in Base 5 — Upper bound on s

There is no (53, 98, 2717)-net in base 5, because

1 times m-reduction [i] would yield (53, 97, 2717)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 63 169489 141045 272112 096679 198972 983450 449322 022991 750634 080675 383625 > 5⁹⁷ [i]