MinT - Best Known (10, 10+35, s)-Nets in Base 5

Best Known (10, 10+35, s)-Nets in Base 5

(10, 10+35, 26)-Net over F₅ — Constructive and digital

Digital (10, 45, 26)-net over F₅, using

t-expansion [i] based on digital (9, 45, 26)-net over F₅, using
- net from sequence [i] based on digital (9, 25)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 9 and N(F) ≥ 26, using
    - an explicitly constructive algebraic function field [i]

(10, 10+35, 27)-Net over F₅ — Digital

Digital (10, 45, 27)-net over F₅, using

net from sequence [i] based on digital (10, 26)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 10 and N(F) ≥ 27, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(10, 10+35, 84)-Net in Base 5 — Upper bound on s

There is no (10, 45, 85)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴⁵, 85, S₅, 35), but
- the linear programming bound shows that MÂ â‰¥ 1 296352 026906 817620 345523 426308 650926 583132 215913 296090 829225 849391 622084 217914 334658 416919 410228 729248 046875 / 44914 337530 635816 671970 749895 802658 083357 856218 754165 656680 133132 092306 360543 > 5⁴⁵ [i]