Best Known (4, 11, s)-Nets in Base 8
(4, 11, 25)-Net over F8 — Constructive and digital
Digital (4, 11, 25)-net over F8, using
- net from sequence [i] based on digital (4, 24)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 4 and N(F) ≥ 25, using
(4, 11, 264)-Net in Base 8 — Upper bound on s
There is no (4, 11, 265)-net in base 8, because
- 1 times m-reduction [i] would yield (4, 10, 265)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1081 110696 > 810 [i]
- extracting embedded orthogonal array [i] would yield OA(810, 265, S8, 6), but
- the linear programming bound shows that M ≥ 59 925125 398528 / 55515 > 810 [i]