Best Known (48, 134, s)-Nets in Base 3
(48, 134, 48)-Net over F3 — Constructive and digital
Digital (48, 134, 48)-net over F3, using
- t-expansion [i] based on digital (45, 134, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(48, 134, 56)-Net over F3 — Digital
Digital (48, 134, 56)-net over F3, using
- t-expansion [i] based on digital (40, 134, 56)-net over F3, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 40 and N(F) ≥ 56, using
- net from sequence [i] based on digital (40, 55)-sequence over F3, using
(48, 134, 165)-Net over F3 — Upper bound on s (digital)
There is no digital (48, 134, 166)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(3134, 166, F3, 86) (dual of [166, 32, 87]-code), but
- construction Y1 [i] would yield
- OA(3133, 150, S3, 86), but
- the linear programming bound shows that M ≥ 10206 967808 467913 747808 389212 583004 511164 705253 854573 732746 285224 754829 / 2 832691 > 3133 [i]
- OA(332, 166, S3, 16), but
- discarding factors would yield OA(332, 156, S3, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 1906 607562 901809 > 332 [i]
- discarding factors would yield OA(332, 156, S3, 16), but
- OA(3133, 150, S3, 86), but
- construction Y1 [i] would yield
(48, 134, 219)-Net in Base 3 — Upper bound on s
There is no (48, 134, 220)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 9887 475553 914173 061073 902333 154526 733132 982790 366654 599646 003025 > 3134 [i]