MinT - Best Known (61−38, 61, s)-Nets in Base 3

Best Known (61−38, 61, s)-Nets in Base 3

(61−38, 61, 32)-Net over F₃ — Constructive and digital

Digital (23, 61, 32)-net over F₃, using

t-expansion [i] based on digital (21, 61, 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]

(61−38, 61, 103)-Net in Base 3 — Upper bound on s

There is no (23, 61, 104)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶¹, 104, S₃, 38), but
- the linear programming bound shows that MÂ â‰¥ 215738 553867 294765 547315 427144 658478 953384 447876 816406 609237 390217 341335 785320 530901 097095 689610 364315 585436 148743 / 1 653900 488288 762417 441699 879030 043019 631369 903205 462657 103479 100855 831115 771782 746875 > 3⁶¹ [i]