Best Known (105−74, 105, s)-Nets in Base 4
(105−74, 105, 34)-Net over F4 — Constructive and digital
Digital (31, 105, 34)-net over F4, using
- t-expansion [i] based on digital (21, 105, 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
(105−74, 105, 43)-Net in Base 4 — Constructive
(31, 105, 43)-net in base 4, using
- t-expansion [i] based on (30, 105, 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
(105−74, 105, 60)-Net over F4 — Digital
Digital (31, 105, 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
(105−74, 105, 145)-Net in Base 4 — Upper bound on s
There is no (31, 105, 146)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(4105, 146, S4, 74), but
- the linear programming bound shows that M ≥ 554775 317608 610115 508612 311219 625428 991296 166157 380060 805003 050440 628272 114981 491927 327224 889344 / 334 386837 125945 971994 944968 167965 > 4105 [i]