MinT - Best Known (28, 28+79, s)-Nets in Base 25

Best Known (28, 28+79, s)-Nets in Base 25

(28, 28+79, 200)-Net over F₂₅ — Constructive and digital

Digital (28, 107, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 107, 200)-net over F₂₅, using
- net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
    - a function field by GarcÃa and Quoos [i]

(28, 28+79, 4022)-Net in Base 25 — Upper bound on s

There is no (28, 107, 4023)-net in base 25, because

1 times m-reduction [i] would yield (28, 106, 4023)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 15227 148479 651699 567756 218778 942706 225943 391417 665604 288249 160008 305401 697169 447221 937261 715105 589028 472444 933797 142308 092602 809345 427107 756376 230425 > 25¹⁰⁶ [i]