Best Known (86, 86+63, s)-Nets in Base 2
(86, 86+63, 54)-Net over F2 — Constructive and digital
Digital (86, 149, 54)-net over F2, using
- 3 times m-reduction [i] based on digital (86, 152, 54)-net over F2, using
- trace code for nets [i] based on digital (10, 76, 27)-net over F4, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 10 and N(F) ≥ 27, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- trace code for nets [i] based on digital (10, 76, 27)-net over F4, using
(86, 86+63, 64)-Net over F2 — Digital
Digital (86, 149, 64)-net over F2, using
(86, 86+63, 295)-Net in Base 2 — Upper bound on s
There is no (86, 149, 296)-net in base 2, because
- 1 times m-reduction [i] would yield (86, 148, 296)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2148, 296, S2, 62), but
- 3 times code embedding in larger space [i] would yield OA(2151, 299, S2, 62), but
- adding a parity check bit [i] would yield OA(2152, 300, S2, 63), but
- the linear programming bound shows that M ≥ 1 822920 957032 908710 300389 173411 682235 603743 600718 371815 426352 372851 396294 641510 983638 017093 363995 208653 722934 746993 732112 453103 710016 735018 198981 581634 152182 044263 594413 848248 874036 866566 735939 553456 835204 576530 181303 910420 691160 014878 461130 563395 780608 / 229 929733 295745 871030 288711 236996 995307 447399 222943 244777 371812 844585 893126 134003 764438 009627 688452 810237 265600 326493 146031 667493 552702 960873 168604 971608 376264 793116 919937 125888 078239 505634 182777 681229 361167 > 2152 [i]
- adding a parity check bit [i] would yield OA(2152, 300, S2, 63), but
- 3 times code embedding in larger space [i] would yield OA(2151, 299, S2, 62), but
- extracting embedded orthogonal array [i] would yield OA(2148, 296, S2, 62), but