Best Known (239−95, 239, s)-Nets in Base 4
(239−95, 239, 138)-Net over F4 — Constructive and digital
Digital (144, 239, 138)-net over F4, using
- 5 times m-reduction [i] based on digital (144, 244, 138)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (21, 71, 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, 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
- digital (21, 71, 34)-net over F4, using
- (u, u+v)-construction [i] based on
(239−95, 239, 139)-Net in Base 4 — Constructive
(144, 239, 139)-net in base 4, using
- (u, u+v)-construction [i] based on
- (24, 71, 35)-net in base 4, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 2 places with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- base expansion [i] based on digital (48, 34)-sequence over F2, using
- net from sequence [i] based on (24, 34)-sequence in base 4, using
- digital (73, 168, 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
- (24, 71, 35)-net in base 4, using
(239−95, 239, 349)-Net over F4 — Digital
Digital (144, 239, 349)-net over F4, using
(239−95, 239, 6811)-Net in Base 4 — Upper bound on s
There is no (144, 239, 6812)-net in base 4, because
- 1 times m-reduction [i] would yield (144, 238, 6812)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 195535 907232 423969 434613 310541 532377 034419 765127 306545 182020 921606 504992 521820 656148 698294 892207 480082 179257 193440 342334 883331 138653 539728 253200 > 4238 [i]