Best Known (153, 253, s)-Nets in Base 4
(153, 253, 138)-Net over F4 — Constructive and digital
Digital (153, 253, 138)-net over F4, using
- t-expansion [i] based on digital (149, 253, 138)-net over F4, using
- 6 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
- 6 times m-reduction [i] based on digital (149, 259, 138)-net over F4, using
(153, 253, 147)-Net in Base 4 — Constructive
(153, 253, 147)-net in base 4, using
- (u, u+v)-construction [i] based on
- (30, 80, 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, 173, 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, 80, 43)-net in base 4, using
(153, 253, 375)-Net over F4 — Digital
Digital (153, 253, 375)-net over F4, using
(153, 253, 7186)-Net in Base 4 — Upper bound on s
There is no (153, 253, 7187)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 210 924499 149823 044476 519485 197369 246379 295018 027570 997559 309620 530862 429924 761684 849749 119423 566175 475157 246936 564576 541297 027226 401328 349437 911063 982048 > 4253 [i]