Best Known (11, ∞, s)-Nets in Base 3
(11, ∞, 20)-Net over F3 — Constructive and digital
Digital (11, m, 20)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (11, 19)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 9, N(F) = 19, and 1 place with degree 3 [i] based on function field F/F3 with g(F) = 9 and N(F) ≥ 19, using an explicitly constructive algebraic function field [i]
(11, ∞, 31)-Net in Base 3 — Upper bound on s
There is no (11, m, 32)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (11, 90, 32)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(390, 32, S3, 3, 79), but
- the LP bound with quadratic polynomials shows that M ≥ 177 468592 551116 819326 458415 416026 789247 509463 / 20 > 390 [i]
- extracting embedded OOA [i] would yield OOA(390, 32, S3, 3, 79), but