MinT - Best Known (28, 28+75, s)-Nets in Base 25

Best Known (28, 28+75, s)-Nets in Base 25

(28, 28+75, 200)-Net over F₂₅ — Constructive and digital

Digital (28, 103, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 103, 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+75, 4340)-Net in Base 25 — Upper bound on s

There is no (28, 103, 4341)-net in base 25, because

1 times m-reduction [i] would yield (28, 102, 4341)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 39084 345805 204764 659659 207852 229107 202050 676031 861868 087043 053247 348944 123644 123564 326661 153158 549965 429648 007411 576200 937396 601659 111947 056985 > 25¹⁰² [i]