Best Known (105−65, 105, s)-Nets in Base 3
(105−65, 105, 42)-Net over F3 — Constructive and digital
Digital (40, 105, 42)-net over F3, using
- t-expansion [i] based on digital (39, 105, 42)-net over F3, using
- net from sequence [i] based on digital (39, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 39 and N(F) ≥ 42, using
- net from sequence [i] based on digital (39, 41)-sequence over F3, using
(105−65, 105, 56)-Net over F3 — Digital
Digital (40, 105, 56)-net over F3, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 40 and N(F) ≥ 56, using
(105−65, 105, 144)-Net in Base 3 — Upper bound on s
There is no (40, 105, 145)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(3105, 145, S3, 65), but
- the linear programming bound shows that M ≥ 2672 696874 555113 070277 370361 668201 700430 711731 822164 429384 303409 602728 450455 / 21 255599 528627 666044 419356 > 3105 [i]