Best Known (82−57, 82, s)-Nets in Base 4
(82−57, 82, 34)-Net over F4 — Constructive and digital
Digital (25, 82, 34)-net over F4, using
- t-expansion [i] based on digital (21, 82, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
(82−57, 82, 35)-Net in Base 4 — Constructive
(25, 82, 35)-net in base 4, using
- t-expansion [i] based on (24, 82, 35)-net in base 4, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
(82−57, 82, 51)-Net over F4 — Digital
Digital (25, 82, 51)-net over F4, using
- net from sequence [i] based on digital (25, 50)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 25 and N(F) ≥ 51, using
(82−57, 82, 146)-Net in Base 4 — Upper bound on s
There is no (25, 82, 147)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(482, 147, S4, 57), but
- the linear programming bound shows that M ≥ 317 037594 874104 788097 363934 385470 033055 949567 295348 251071 808033 395027 252472 917734 505583 665296 587433 584079 322091 728288 179828 060163 502846 553034 526452 257111 175653 922741 542240 051385 314719 039488 / 12 974914 487478 534018 893942 165576 018487 860552 476600 082829 690910 525536 318801 189236 245587 024898 169738 332511 320472 102082 003724 381476 705681 480945 > 482 [i]