Best Known (44, 44+166, s)-Nets in Base 3
(44, 44+166, 42)-Net over F3 — Constructive and digital
Digital (44, 210, 42)-net over F3, using
- t-expansion [i] based on digital (39, 210, 42)-net over F3, using
- net from sequence [i] based on digital (39, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 39 and N(F) ≥ 42, using
- net from sequence [i] based on digital (39, 41)-sequence over F3, using
(44, 44+166, 56)-Net over F3 — Digital
Digital (44, 210, 56)-net over F3, using
- t-expansion [i] based on digital (40, 210, 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
(44, 44+166, 140)-Net in Base 3 — Upper bound on s
There is no (44, 210, 141)-net in base 3, because
- 82 times m-reduction [i] would yield (44, 128, 141)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3128, 141, S3, 84), but
- the linear programming bound shows that M ≥ 8 586449 512614 255704 906677 599653 756381 172136 834518 319080 363152 884431 / 524875 > 3128 [i]
- extracting embedded orthogonal array [i] would yield OA(3128, 141, S3, 84), but