Best Known (16, 16+38, s)-Nets in Base 4
(16, 16+38, 33)-Net over F4 — Constructive and digital
Digital (16, 54, 33)-net over F4, using
- t-expansion [i] based on digital (15, 54, 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
(16, 16+38, 36)-Net over F4 — Digital
Digital (16, 54, 36)-net over F4, using
- net from sequence [i] based on digital (16, 35)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 16 and N(F) ≥ 36, using
(16, 16+38, 109)-Net in Base 4 — Upper bound on s
There is no (16, 54, 110)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(454, 110, S4, 38), but
- the linear programming bound shows that M ≥ 135 440741 241049 789665 781637 668704 693714 181378 635930 680120 605353 901214 137048 253327 764568 928839 792611 860867 861927 895921 547923 172302 991740 487447 699778 622739 218992 187171 037940 404594 079385 195853 250698 475651 203072 / 411109 861116 068119 672276 253441 803189 139344 068142 940724 691170 543488 982695 077949 102293 311726 472930 596418 877717 472747 798405 384755 565158 675189 243095 201237 990465 277532 513505 255427 > 454 [i]