Best Known (3, ∞, s)-Nets in Base 27
(3, ∞, 52)-Net over F27 — Constructive and digital
Digital (3, m, 52)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
(3, ∞, 56)-Net over F27 — Digital
Digital (3, m, 56)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (3, 55)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 56, using
(3, ∞, 102)-Net in Base 27 — Upper bound on s
There is no (3, m, 103)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (3, 97, 103)-net in base 27, but
- extracting embedded orthogonal array [i] would yield OA(2797, 103, S27, 94), but
- the linear programming bound shows that M ≥ 128 911025 055144 003712 512083 846133 074073 104655 021247 977332 109220 807942 928575 240457 586722 133506 291651 511625 988777 715999 325631 713723 671307 153546 411869 / 17 583797 > 2797 [i]
- extracting embedded orthogonal array [i] would yield OA(2797, 103, S27, 94), but