Best Known (123−121, 123, s)-Nets in Base 8
(123−121, 123, 17)-Net over F8 — Constructive and digital
Digital (2, 123, 17)-net over F8, using
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 17, using
(123−121, 123, 18)-Net over F8 — Digital
Digital (2, 123, 18)-net over F8, using
- net from sequence [i] based on digital (2, 17)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 2 and N(F) ≥ 18, using
(123−121, 123, 23)-Net in Base 8 — Upper bound on s
There is no (2, 123, 24)-net in base 8, because
- 96 times m-reduction [i] would yield (2, 27, 24)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(827, 24, S8, 2, 25), but
- the linear programming bound for OOAs shows that M ≥ 1329 818401 576092 092176 793600 / 513 > 827 [i]
- extracting embedded OOA [i] would yield OOA(827, 24, S8, 2, 25), but