Best Known (145, 235, s)-Nets in Base 4
(145, 235, 138)-Net over F4 — Constructive and digital
Digital (145, 235, 138)-net over F4, using
- 12 times m-reduction [i] based on digital (145, 247, 138)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (21, 72, 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, 175, 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, 72, 34)-net over F4, using
- (u, u+v)-construction [i] based on
(145, 235, 146)-Net in Base 4 — Constructive
(145, 235, 146)-net in base 4, using
- (u, u+v)-construction [i] based on
- (27, 72, 42)-net in base 4, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- base expansion [i] based on digital (54, 41)-sequence over F2, using
- net from sequence [i] based on (27, 41)-sequence in base 4, using
- digital (73, 163, 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
- (27, 72, 42)-net in base 4, using
(145, 235, 389)-Net over F4 — Digital
Digital (145, 235, 389)-net over F4, using
(145, 235, 8150)-Net in Base 4 — Upper bound on s
There is no (145, 235, 8151)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3058 402623 671267 681477 833754 731365 723379 340804 773772 018470 426181 238053 903479 340021 042494 579379 252033 176186 311136 345454 479711 122310 358917 643512 > 4235 [i]