Best Known (90−62, 90, s)-Nets in Base 5
(90−62, 90, 51)-Net over F5 — Constructive and digital
Digital (28, 90, 51)-net over F5, using
- t-expansion [i] based on digital (22, 90, 51)-net over F5, using
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 22 and N(F) ≥ 51, using
- net from sequence [i] based on digital (22, 50)-sequence over F5, using
(90−62, 90, 55)-Net over F5 — Digital
Digital (28, 90, 55)-net over F5, using
- t-expansion [i] based on digital (23, 90, 55)-net over F5, using
- net from sequence [i] based on digital (23, 54)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 23 and N(F) ≥ 55, using
- net from sequence [i] based on digital (23, 54)-sequence over F5, using
(90−62, 90, 299)-Net in Base 5 — Upper bound on s
There is no (28, 90, 300)-net in base 5, because
- 1 times m-reduction [i] would yield (28, 89, 300)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(589, 300, S5, 61), but
- the linear programming bound shows that M ≥ 26678 246010 631137 429760 418376 617904 570436 960106 095146 950890 830576 146755 007586 898296 859601 342474 903656 670494 077879 710048 684103 185223 648324 608802 795410 156250 / 135 254019 495799 314939 492565 807491 240984 869091 107317 550744 938298 709709 984177 006612 981474 880681 > 589 [i]
- extracting embedded orthogonal array [i] would yield OA(589, 300, S5, 61), but