Best Known (45, 120, s)-Nets in Base 3
(45, 120, 48)-Net over F3 — Constructive and digital
Digital (45, 120, 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
(45, 120, 56)-Net over F3 — Digital
Digital (45, 120, 56)-net over F3, using
- t-expansion [i] based on digital (40, 120, 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
(45, 120, 180)-Net over F3 — Upper bound on s (digital)
There is no digital (45, 120, 181)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(3120, 181, F3, 75) (dual of [181, 61, 76]-code), but
- construction Y1 [i] would yield
- OA(3119, 147, S3, 75), but
- the linear programming bound shows that M ≥ 16 137915 552723 745131 682214 391750 091116 522557 190679 736158 328855 711764 240731 / 23372 130007 496452 > 3119 [i]
- OA(361, 181, S3, 34), but
- discarding factors would yield OA(361, 176, S3, 34), but
- the linear programming bound shows that M ≥ 812 356626 791711 438639 003017 318488 339021 708011 289038 629210 828125 / 5801 809430 490682 982977 100374 687357 > 361 [i]
- discarding factors would yield OA(361, 176, S3, 34), but
- OA(3119, 147, S3, 75), but
- construction Y1 [i] would yield
(45, 120, 216)-Net in Base 3 — Upper bound on s
There is no (45, 120, 217)-net in base 3, because
- 1 times m-reduction [i] would yield (45, 119, 217)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 654 638524 372023 414877 758292 895346 269335 981374 255100 133283 > 3119 [i]