Best Known (120−88, 120, s)-Nets in Base 4
(120−88, 120, 34)-Net over F4 — Constructive and digital
Digital (32, 120, 34)-net over F4, using
- t-expansion [i] based on digital (21, 120, 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
(120−88, 120, 43)-Net in Base 4 — Constructive
(32, 120, 43)-net in base 4, using
- t-expansion [i] based on (30, 120, 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
(120−88, 120, 60)-Net over F4 — Digital
Digital (32, 120, 60)-net over F4, using
- t-expansion [i] based on digital (31, 120, 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
(120−88, 120, 133)-Net in Base 4 — Upper bound on s
There is no (32, 120, 134)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(4120, 134, S4, 88), but
- the linear programming bound shows that M ≥ 44879 226248 006156 277409 262412 286361 464349 961201 014006 795486 400435 014006 889500 377088 / 21749 419055 > 4120 [i]