Best Known (32, 32+83, s)-Nets in Base 4
(32, 32+83, 34)-Net over F4 — Constructive and digital
Digital (32, 115, 34)-net over F4, using
- t-expansion [i] based on digital (21, 115, 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
(32, 32+83, 43)-Net in Base 4 — Constructive
(32, 115, 43)-net in base 4, using
- t-expansion [i] based on (30, 115, 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
(32, 32+83, 60)-Net over F4 — Digital
Digital (32, 115, 60)-net over F4, using
- t-expansion [i] based on digital (31, 115, 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
(32, 32+83, 135)-Net in Base 4 — Upper bound on s
There is no (32, 115, 136)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(4115, 136, S4, 83), but
- the linear programming bound shows that M ≥ 3 852173 251108 596842 384779 441761 266970 500973 282081 261933 174545 595282 974135 341159 546880 / 2018 969268 695379 > 4115 [i]