MinT - Best Known (69−47, 69, s)-Nets in Base 5

Best Known (69−47, 69, s)-Nets in Base 5

(69−47, 69, 51)-Net over F₅ — Constructive and digital

Digital (22, 69, 51)-net over F₅, using

net from sequence [i] based on digital (22, 50)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
  - an explicitly constructive algebraic function field [i]

(69−47, 69, 257)-Net in Base 5 — Upper bound on s

There is no (22, 69, 258)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁶⁹, 258, S₅, 47), but
- the linear programming bound shows that MÂ â‰¥ 276210 913798 273108 499334 802809 090336 164877 514757 757620 970595 389304 685622 007970 147130 819356 107167 550362 646579 742431 640625 / 157185 561275 733120 446695 766534 495522 825051 712666 265298 479348 466622 663806 > 5⁶⁹ [i]