Best Known (43−28, 43, s)-Nets in Base 3
(43−28, 43, 28)-Net over F3 — Constructive and digital
Digital (15, 43, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
(43−28, 43, 60)-Net over F3 — Upper bound on s (digital)
There is no digital (15, 43, 61)-net over F3, because
- 1 times m-reduction [i] would yield digital (15, 42, 61)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(342, 61, F3, 27) (dual of [61, 19, 28]-code), but
- residual code [i] would yield linear OA(315, 33, F3, 9) (dual of [33, 18, 10]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(342, 61, F3, 27) (dual of [61, 19, 28]-code), but
(43−28, 43, 67)-Net in Base 3 — Upper bound on s
There is no (15, 43, 68)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(343, 68, S3, 28), but
- the linear programming bound shows that M ≥ 15 309075 649282 585984 320219 610288 301331 / 40873 610548 490720 > 343 [i]