MinT - Best Known (59−37, 59, s)-Nets in Base 3

Best Known (59−37, 59, s)-Nets in Base 3

(59−37, 59, 32)-Net over F₃ — Constructive and digital

Digital (22, 59, 32)-net over F₃, using

t-expansion [i] based on digital (21, 59, 32)-net over F₃, using
- net from sequence [i] based on digital (21, 31)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
    - an explicitly constructive algebraic function field [i]

(59−37, 59, 97)-Net in Base 3 — Upper bound on s

There is no (22, 59, 98)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁵⁹, 98, S₃, 37), but
- the linear programming bound shows that MÂ â‰¥ 669 706575 926673 602832 294393 126699 440696 899104 765650 881469 270113 504934 632053 / 45175 106642 610955 544989 816374 596571 195177 978293 > 3⁵⁹ [i]