Best Known (142−111, 142, s)-Nets in Base 4
(142−111, 142, 34)-Net over F4 — Constructive and digital
Digital (31, 142, 34)-net over F4, using
- t-expansion [i] based on digital (21, 142, 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
(142−111, 142, 43)-Net in Base 4 — Constructive
(31, 142, 43)-net in base 4, using
- t-expansion [i] based on (30, 142, 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
(142−111, 142, 60)-Net over F4 — Digital
Digital (31, 142, 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
(142−111, 142, 129)-Net in Base 4 — Upper bound on s
There is no (31, 142, 130)-net in base 4, because
- 26 times m-reduction [i] would yield (31, 116, 130)-net in base 4, but
- extracting embedded orthogonal array [i] would yield OA(4116, 130, S4, 85), but
- the linear programming bound shows that M ≥ 2910 853909 303427 843179 867153 014027 057557 909168 265288 524176 409407 780925 198594 736128 / 395256 842585 > 4116 [i]
- extracting embedded orthogonal array [i] would yield OA(4116, 130, S4, 85), but