Best Known (128−102, 128, s)-Nets in Base 16
(128−102, 128, 65)-Net over F16 — Constructive and digital
Digital (26, 128, 65)-net over F16, using
- t-expansion [i] based on digital (6, 128, 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
(128−102, 128, 66)-Net in Base 16 — Constructive
(26, 128, 66)-net in base 16, using
- t-expansion [i] based on (25, 128, 66)-net in base 16, using
- net from sequence [i] based on (25, 65)-sequence in base 16, using
- base expansion [i] based on digital (50, 65)-sequence over F4, using
- t-expansion [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 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) = 49 and N(F) ≥ 66, using
- t-expansion [i] based on digital (49, 65)-sequence over F4, using
- base expansion [i] based on digital (50, 65)-sequence over F4, using
- net from sequence [i] based on (25, 65)-sequence in base 16, using
(128−102, 128, 150)-Net over F16 — Digital
Digital (26, 128, 150)-net over F16, using
- net from sequence [i] based on digital (26, 149)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 26 and N(F) ≥ 150, using
(128−102, 128, 1364)-Net in Base 16 — Upper bound on s
There is no (26, 128, 1365)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 13665 271826 467174 387923 693567 717292 698963 038175 027090 810242 166570 768480 772114 664219 740014 487802 182859 070007 308520 719159 182713 021772 821358 745323 213933 937976 > 16128 [i]