Best Known (152−126, 152, s)-Nets in Base 3
(152−126, 152, 36)-Net over F3 — Constructive and digital
Digital (26, 152, 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
(152−126, 152, 37)-Net over F3 — Digital
Digital (26, 152, 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]
(152−126, 152, 68)-Net in Base 3 — Upper bound on s
There is no (26, 152, 69)-net in base 3, because
- 20 times m-reduction [i] would yield (26, 132, 69)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3132, 69, S3, 2, 106), but
- the LP bound with quadratic polynomials shows that M ≥ 111735 579243 228552 716503 312107 606439 394632 411259 998146 190911 899397 / 107 > 3132 [i]
- extracting embedded OOA [i] would yield OOA(3132, 69, S3, 2, 106), but