MinT - Best Known (85−49, 85, s)-Nets in Base 25

Best Known (85−49, 85, s)-Nets in Base 25

(85−49, 85, 208)-Net over F₂₅ — Constructive and digital

Digital (36, 85, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 85, 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]

(85−49, 85, 224)-Net over F₂₅ — Digital

Digital (36, 85, 224)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−49, 85, 31898)-Net in Base 25 — Upper bound on s

There is no (36, 85, 31899)-net in base 25, because

1 times m-reduction [i] would yield (36, 84, 31899)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2673 603564 416416 145104 922858 025839 315943 423341 574966 157018 445403 262606 113718 833657 936681 113160 455439 775592 387470 905025 > 25⁸⁴ [i]