Best Known (19, 19+32, s)-Nets in Base 3
(19, 19+32, 28)-Net over F3 — Constructive and digital
Digital (19, 51, 28)-net over F3, using
- t-expansion [i] based on digital (15, 51, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
(19, 19+32, 32)-Net over F3 — Digital
Digital (19, 51, 32)-net over F3, using
- net from sequence [i] based on digital (19, 31)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 19 and N(F) ≥ 32, using
(19, 19+32, 90)-Net in Base 3 — Upper bound on s
There is no (19, 51, 91)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(351, 91, S3, 32), but
- the linear programming bound shows that M ≥ 3 796003 121606 659684 644081 485270 254802 809922 702083 145243 272087 278428 845740 570091 586803 340207 313946 354006 591960 625547 / 1 756668 470243 430645 991636 297238 233510 101788 678484 940922 765709 380449 381903 813470 038571 507115 > 351 [i]