Best Known (20, 20+47, s)-Nets in Base 4
(20, 20+47, 33)-Net over F4 — Constructive and digital
Digital (20, 67, 33)-net over F4, using
- t-expansion [i] based on digital (15, 67, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
(20, 20+47, 41)-Net over F4 — Digital
Digital (20, 67, 41)-net over F4, using
- t-expansion [i] based on digital (18, 67, 41)-net over F4, using
- net from sequence [i] based on digital (18, 40)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 18 and N(F) ≥ 41, using
- net from sequence [i] based on digital (18, 40)-sequence over F4, using
(20, 20+47, 122)-Net in Base 4 — Upper bound on s
There is no (20, 67, 123)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(467, 123, S4, 47), but
- the linear programming bound shows that M ≥ 43402 647924 975488 920450 003944 566378 964570 407885 930315 158568 274900 052775 055729 425702 074252 778284 519466 230412 079171 949623 812197 935803 959581 270319 073009 003679 424611 406027 085968 310272 / 1 972722 979992 492582 380725 903751 953752 652629 461130 906381 054114 627794 331612 476321 726116 126868 678992 555081 191829 266311 527075 509736 859232 980625 > 467 [i]