Best Known (152, 251, s)-Nets in Base 4
(152, 251, 138)-Net over F4 — Constructive and digital
Digital (152, 251, 138)-net over F4, using
- t-expansion [i] based on digital (149, 251, 138)-net over F4, using
- 8 times m-reduction [i] based on digital (149, 259, 138)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (21, 76, 34)-net over F4, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- T5 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 21 and N(F) ≥ 34, using
- net from sequence [i] based on digital (21, 33)-sequence over F4, using
- digital (73, 183, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- digital (21, 76, 34)-net over F4, using
- (u, u+v)-construction [i] based on
- 8 times m-reduction [i] based on digital (149, 259, 138)-net over F4, using
(152, 251, 147)-Net in Base 4 — Constructive
(152, 251, 147)-net in base 4, using
- (u, u+v)-construction [i] based on
- (30, 79, 43)-net in base 4, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- base expansion [i] based on digital (60, 42)-sequence over F2, using
- net from sequence [i] based on (30, 42)-sequence in base 4, using
- digital (73, 172, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- (30, 79, 43)-net in base 4, using
(152, 251, 374)-Net over F4 — Digital
Digital (152, 251, 374)-net over F4, using
(152, 251, 7474)-Net in Base 4 — Upper bound on s
There is no (152, 251, 7475)-net in base 4, because
- 1 times m-reduction [i] would yield (152, 250, 7475)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 3 281457 872235 591204 672433 477726 420986 172288 691213 236523 547223 950148 127304 206122 100941 326878 883474 663589 431543 792809 717254 777620 649800 665446 970597 444938 > 4250 [i]