Best Known (2, 2+∞, s)-Nets in Base 27
(2, 2+∞, 48)-Net over F27 — Constructive and digital
Digital (2, m, 48)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
(2, 2+∞, 77)-Net in Base 27 — Upper bound on s
There is no (2, m, 78)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (2, 74, 78)-net in base 27, but
- extracting embedded orthogonal array [i] would yield OA(2774, 78, S27, 72), but
- the linear programming bound shows that M ≥ 981 000392 047679 793224 589514 892092 100547 285178 849241 756604 164607 128464 559760 391182 392033 793658 959804 539641 190037 / 106799 > 2774 [i]
- extracting embedded orthogonal array [i] would yield OA(2774, 78, S27, 72), but