Best Known (105−75, 105, s)-Nets in Base 5
(105−75, 105, 51)-Net over F5 — Constructive and digital
Digital (30, 105, 51)-net over F5, using
- t-expansion [i] based on digital (22, 105, 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
(105−75, 105, 58)-Net over F5 — Digital
Digital (30, 105, 58)-net over F5, using
- net from sequence [i] based on digital (30, 57)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 30 and N(F) ≥ 58, using
(105−75, 105, 298)-Net in Base 5 — Upper bound on s
There is no (30, 105, 299)-net in base 5, because
- 3 times m-reduction [i] would yield (30, 102, 299)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5102, 299, S5, 72), but
- 1 times code embedding in larger space [i] would yield OA(5103, 300, S5, 72), but
- the linear programming bound shows that M ≥ 478 901718 105137 911610 313547 927456 422385 722345 743553 984250 169924 586587 170932 338603 362596 903988 648129 309869 595013 750020 588871 217191 057522 338810 640555 106897 465447 158636 062062 079931 966010 972366 372400 177425 561196 287162 601947 784423 828125 / 401 197824 075026 459436 067150 186574 959415 181970 908957 232051 628167 198395 361766 342434 416944 913521 501110 020479 954253 877089 689554 355276 130592 474729 565008 970767 782757 > 5103 [i]
- 1 times code embedding in larger space [i] would yield OA(5103, 300, S5, 72), but
- extracting embedded orthogonal array [i] would yield OA(5102, 299, S5, 72), but