MinT - Best Known (47−37, 47, s)-Nets in Base 5

Best Known (47−37, 47, s)-Nets in Base 5

(47−37, 47, 26)-Net over F₅ — Constructive and digital

Digital (10, 47, 26)-net over F₅, using

t-expansion [i] based on digital (9, 47, 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]

(47−37, 47, 27)-Net over F₅ — Digital

Digital (10, 47, 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]

(47−37, 47, 74)-Net in Base 5 — Upper bound on s

There is no (10, 47, 75)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴⁷, 75, S₅, 37), but
- the linear programming bound shows that MÂ â‰¥ 3044 972730 479255 975508 312559 441037 592478 096485 137939 453125 / 4 148614 698181 499353 338432 > 5⁴⁷ [i]