Best Known (24−21, 24, s)-Nets in Base 8
(24−21, 24, 24)-Net over F8 — Constructive and digital
Digital (3, 24, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
(24−21, 24, 67)-Net in Base 8 — Upper bound on s
There is no (3, 24, 68)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(824, 68, S8, 21), but
- the linear programming bound shows that M ≥ 290703 502804 494806 349566 860182 159360 / 60 209408 898671 > 824 [i]