Best Known (109−77, 109, s)-Nets in Base 4
(109−77, 109, 34)-Net over F4 — Constructive and digital
Digital (32, 109, 34)-net over F4, using
- t-expansion [i] based on digital (21, 109, 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
(109−77, 109, 43)-Net in Base 4 — Constructive
(32, 109, 43)-net in base 4, using
- t-expansion [i] based on (30, 109, 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
(109−77, 109, 60)-Net over F4 — Digital
Digital (32, 109, 60)-net over F4, using
- t-expansion [i] based on digital (31, 109, 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
(109−77, 109, 147)-Net in Base 4 — Upper bound on s
There is no (32, 109, 148)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(4109, 148, S4, 77), but
- the linear programming bound shows that M ≥ 93369 878733 386831 807951 664767 066779 195616 328505 480197 805811 746625 475920 186816 273170 627753 565380 149248 / 221551 214490 977896 234087 779488 628125 > 4109 [i]