Best Known (140, 140+97, s)-Nets in Base 4
(140, 140+97, 137)-Net over F4 — Constructive and digital
Digital (140, 237, 137)-net over F4, using
- 7 times m-reduction [i] based on digital (140, 244, 137)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (15, 67, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- digital (73, 177, 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 (15, 67, 33)-net over F4, using
- (u, u+v)-construction [i] based on
(140, 140+97, 316)-Net over F4 — Digital
Digital (140, 237, 316)-net over F4, using
(140, 140+97, 5659)-Net in Base 4 — Upper bound on s
There is no (140, 237, 5660)-net in base 4, because
- 1 times m-reduction [i] would yield (140, 236, 5660)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 12237 534945 901018 515837 635940 317845 176403 918066 748249 297147 913471 625466 324200 924229 018071 468929 984253 185596 468099 290791 262417 066665 915992 322448 > 4236 [i]