Best Known (61, 136, s)-Nets in Base 8
(61, 136, 111)-Net over F8 — Constructive and digital
Digital (61, 136, 111)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (10, 47, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- digital (14, 89, 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 (10, 47, 46)-net over F8, using
(61, 136, 151)-Net over F8 — Digital
Digital (61, 136, 151)-net over F8, using
(61, 136, 156)-Net in Base 8
(61, 136, 156)-net in base 8, using
- base change [i] based on digital (27, 102, 156)-net over F16, using
- net from sequence [i] based on digital (27, 155)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 27 and N(F) ≥ 156, using
- net from sequence [i] based on digital (27, 155)-sequence over F16, using
(61, 136, 4106)-Net in Base 8 — Upper bound on s
There is no (61, 136, 4107)-net in base 8, because
- 1 times m-reduction [i] would yield (61, 135, 4107)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 83 367808 370388 619379 868965 485217 042127 924947 323654 884311 527212 546402 433891 960190 651008 988182 333832 871039 969507 335795 795456 > 8135 [i]