MinT - Best Known (86−50, 86, s)-Nets in Base 25

Best Known (86−50, 86, s)-Nets in Base 25

(86−50, 86, 208)-Net over F₂₅ — Constructive and digital

Digital (36, 86, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 86, 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]

(86−50, 86, 216)-Net over F₂₅ — Digital

Digital (36, 86, 216)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(86−50, 86, 27297)-Net in Base 25 — Upper bound on s

There is no (36, 86, 27298)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1 671442 406542 945518 642808 789225 566530 546921 113034 085581 365660 633087 592292 060354 394781 795298 000624 229472 108516 765362 373809 > 25⁸⁶ [i]