Best Known (83−51, 83, s)-Nets in Base 4
(83−51, 83, 34)-Net over F4 — Constructive and digital
Digital (32, 83, 34)-net over F4, using
- t-expansion [i] based on digital (21, 83, 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
(83−51, 83, 43)-Net in Base 4 — Constructive
(32, 83, 43)-net in base 4, using
- t-expansion [i] based on (30, 83, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
(83−51, 83, 60)-Net over F4 — Digital
Digital (32, 83, 60)-net over F4, using
- t-expansion [i] based on digital (31, 83, 60)-net over F4, using
- net from sequence [i] based on digital (31, 59)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 31 and N(F) ≥ 60, using
- net from sequence [i] based on digital (31, 59)-sequence over F4, using
(83−51, 83, 299)-Net in Base 4 — Upper bound on s
There is no (32, 83, 300)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(483, 300, S4, 51), but
- the linear programming bound shows that M ≥ 8 669464 869261 106850 173136 291210 866790 740193 996403 412994 618413 203155 733105 093782 117120 984436 609117 895272 047515 898971 422720 / 88104 048654 161452 142075 042836 554792 583523 738651 953284 684543 981610 834621 > 483 [i]