Best Known (28, 72, s)-Nets in Base 3
(28, 72, 37)-Net over F3 — Constructive and digital
Digital (28, 72, 37)-net over F3, using
- t-expansion [i] based on digital (27, 72, 37)-net over F3, using
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 26, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
(28, 72, 39)-Net over F3 — Digital
Digital (28, 72, 39)-net over F3, using
- t-expansion [i] based on digital (27, 72, 39)-net over F3, using
- net from sequence [i] based on digital (27, 38)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 27 and N(F) ≥ 39, using
- net from sequence [i] based on digital (27, 38)-sequence over F3, using
(28, 72, 128)-Net in Base 3 — Upper bound on s
There is no (28, 72, 129)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(372, 129, S3, 44), but
- the linear programming bound shows that M ≥ 44581 042680 190201 424193 831840 753900 670798 725450 637402 342191 554654 268694 860799 351692 628249 035083 768310 785141 170441 602743 910081 150638 796780 311369 419178 341421 989330 024725 427166 876875 682423 121951 240264 500151 / 1 947482 853721 425586 922187 925058 224422 649757 526790 464738 458184 631778 914633 064948 606561 512864 131931 488340 022430 458898 125986 767827 041137 500285 991795 319155 347570 902673 254730 > 372 [i]