Best Known (26, 79, s)-Nets in Base 3
(26, 79, 36)-Net over F3 — Constructive and digital
Digital (26, 79, 36)-net over F3, using
- net from sequence [i] based on digital (26, 35)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using
(26, 79, 37)-Net over F3 — Digital
Digital (26, 79, 37)-net over F3, using
- net from sequence [i] based on digital (26, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 25, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 25 and N(F) ≥ 36, using algebraic function fields over ℤ3 by Niederreiter/Xing [i]
(26, 79, 88)-Net in Base 3 — Upper bound on s
There is no (26, 79, 89)-net in base 3, because
- 2 times m-reduction [i] would yield (26, 77, 89)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(377, 89, S3, 51), but
- the linear programming bound shows that M ≥ 234 050699 303904 924847 394964 782291 553868 957869 / 34 944520 > 377 [i]
- extracting embedded orthogonal array [i] would yield OA(377, 89, S3, 51), but