MinT - Best Known (36, 109, s)-Nets in Base 25

Best Known (36, 109, s)-Nets in Base 25

(36, 109, 208)-Net over F₂₅ — Constructive and digital

Digital (36, 109, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 109, 208)-net over F₂₅, using
- net from sequence [i] based on digital (35, 207)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 35 and N(F) ≥ 208, using
    - a function field by GarcÃa and Quoos [i]

(36, 109, 9278)-Net in Base 25 — Upper bound on s

There is no (36, 109, 9279)-net in base 25, because

1 times m-reduction [i] would yield (36, 108, 9279)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 9 529680 982979 074321 638144 526726 914207 126048 306422 829528 272277 895553 382874 674211 513237 638917 340061 128754 862615 495601 123765 900235 275164 482483 238451 160225 > 25¹⁰⁸ [i]