Best Known (20, 20+62, s)-Nets in Base 5
(20, 20+62, 43)-Net over F5 — Constructive and digital
Digital (20, 82, 43)-net over F5, using
- t-expansion [i] based on digital (18, 82, 43)-net over F5, using
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
(20, 20+62, 45)-Net over F5 — Digital
Digital (20, 82, 45)-net over F5, using
- t-expansion [i] based on digital (19, 82, 45)-net over F5, using
- net from sequence [i] based on digital (19, 44)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 19 and N(F) ≥ 45, using
- net from sequence [i] based on digital (19, 44)-sequence over F5, using
(20, 20+62, 141)-Net in Base 5 — Upper bound on s
There is no (20, 82, 142)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(582, 142, S5, 62), but
- the linear programming bound shows that M ≥ 26 632350 405437 081035 322526 630902 397045 504861 156096 118274 162235 874959 657637 072050 166840 579958 188640 538141 938536 969799 217608 333373 198278 983288 810975 529318 600288 179730 295468 061740 393750 369548 797607 421875 / 12145 652492 090771 148617 172025 872130 924350 173191 879543 358302 157165 601918 788945 406191 605367 680642 629077 796636 084568 217604 909721 616324 496645 725619 > 582 [i]