Best Known (77−41, 77, s)-Nets in Base 8
(77−41, 77, 82)-Net over F8 — Constructive and digital
Digital (36, 77, 82)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (2, 22, 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
- net from sequence [i] based on digital (2, 16)-sequence over F8, using
- digital (14, 55, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (2, 22, 17)-net over F8, using
(77−41, 77, 112)-Net over F8 — Digital
Digital (36, 77, 112)-net over F8, using
- t-expansion [i] based on digital (35, 77, 112)-net over F8, using
- net from sequence [i] based on digital (35, 111)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 35 and N(F) ≥ 112, using
- net from sequence [i] based on digital (35, 111)-sequence over F8, using
(77−41, 77, 3193)-Net in Base 8 — Upper bound on s
There is no (36, 77, 3194)-net in base 8, because
- 1 times m-reduction [i] would yield (36, 76, 3194)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 432 547584 697323 662132 085619 219906 823119 448815 064753 900315 801624 468198 > 876 [i]