Best Known (23−21, 23, s)-Nets in Base 27
(23−21, 23, 48)-Net over F27 — Constructive and digital
Digital (2, 23, 48)-net over F27, 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
(23−21, 23, 236)-Net in Base 27 — Upper bound on s
There is no (2, 23, 237)-net in base 27, because
- 5 times m-reduction [i] would yield (2, 18, 237)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 58 533621 534559 819557 182625 > 2718 [i]
- extracting embedded orthogonal array [i] would yield OA(2718, 237, S27, 16), but
- the linear programming bound shows that M ≥ 8574 818556 878926 048835 645461 849665 492253 619472 / 145 328002 696337 581343 > 2718 [i]