Best Known (161−128, 161, s)-Nets in Base 3
(161−128, 161, 38)-Net over F3 — Constructive and digital
Digital (33, 161, 38)-net over F3, using
- t-expansion [i] based on digital (32, 161, 38)-net over F3, using
- net from sequence [i] based on digital (32, 37)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 32 and N(F) ≥ 38, using
- net from sequence [i] based on digital (32, 37)-sequence over F3, using
(161−128, 161, 46)-Net over F3 — Digital
Digital (33, 161, 46)-net over F3, using
- net from sequence [i] based on digital (33, 45)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 33 and N(F) ≥ 46, using
(161−128, 161, 107)-Net over F3 — Upper bound on s (digital)
There is no digital (33, 161, 108)-net over F3, because
- 59 times m-reduction [i] would yield digital (33, 102, 108)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(3102, 108, F3, 69) (dual of [108, 6, 70]-code), but
(161−128, 161, 108)-Net in Base 3 — Upper bound on s
There is no (33, 161, 109)-net in base 3, because
- 64 times m-reduction [i] would yield (33, 97, 109)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(397, 109, S3, 64), but
- the linear programming bound shows that M ≥ 13 468083 991561 019023 891072 124538 296580 900734 840712 818463 / 597 447695 > 397 [i]
- extracting embedded orthogonal array [i] would yield OA(397, 109, S3, 64), but