Best Known (140, 140+72, s)-Nets in Base 4
(140, 140+72, 163)-Net over F4 — Constructive and digital
Digital (140, 212, 163)-net over F4, using
- t-expansion [i] based on digital (139, 212, 163)-net over F4, using
- 2 times m-reduction [i] based on digital (139, 214, 163)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (15, 52, 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 (87, 162, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 81, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 81, 65)-net over F16, using
- digital (15, 52, 33)-net over F4, using
- (u, u+v)-construction [i] based on
- 2 times m-reduction [i] based on digital (139, 214, 163)-net over F4, using
(140, 140+72, 240)-Net in Base 4 — Constructive
(140, 212, 240)-net in base 4, using
- 2 times m-reduction [i] based on (140, 214, 240)-net in base 4, using
- trace code for nets [i] based on (33, 107, 120)-net in base 16, using
- 3 times m-reduction [i] based on (33, 110, 120)-net in base 16, using
- base change [i] based on digital (11, 88, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- base change [i] based on digital (11, 88, 120)-net over F32, using
- 3 times m-reduction [i] based on (33, 110, 120)-net in base 16, using
- trace code for nets [i] based on (33, 107, 120)-net in base 16, using
(140, 140+72, 541)-Net over F4 — Digital
Digital (140, 212, 541)-net over F4, using
(140, 140+72, 16684)-Net in Base 4 — Upper bound on s
There is no (140, 212, 16685)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 43 368397 395187 415768 600753 190765 631791 086260 717429 036247 954375 755529 069775 024324 068264 847216 534735 912733 711490 276625 348273 730795 > 4212 [i]