MinT - Best Known (44−34, 44, s)-Nets in Base 5

Best Known (44−34, 44, s)-Nets in Base 5

(44−34, 44, 26)-Net over F₅ — Constructive and digital

Digital (10, 44, 26)-net over F₅, using

t-expansion [i] based on digital (9, 44, 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]

(44−34, 44, 27)-Net over F₅ — Digital

Digital (10, 44, 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]

(44−34, 44, 89)-Net in Base 5 — Upper bound on s

There is no (10, 44, 90)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴⁴, 90, S₅, 34), but
- the linear programming bound shows that MÂ â‰¥ 24 192417 062922 885005 933596 322873 037411 669566 714955 542183 606156 756978 202689 694939 281344 924849 008748 424239 456653 594970 703125 / 4 086320 290100 252203 029440 439018 111737 079146 161342 839533 919881 144670 105506 170956 210872 419397 > 5⁴⁴ [i]