Best Known (129−102, 129, s)-Nets in Base 16
(129−102, 129, 65)-Net over F16 — Constructive and digital
Digital (27, 129, 65)-net over F16, using
- t-expansion [i] based on digital (6, 129, 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
(129−102, 129, 66)-Net in Base 16 — Constructive
(27, 129, 66)-net in base 16, using
- t-expansion [i] based on (25, 129, 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
(129−102, 129, 156)-Net over F16 — Digital
Digital (27, 129, 156)-net over F16, using
- net from sequence [i] based on digital (27, 155)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 27 and N(F) ≥ 156, using
(129−102, 129, 1442)-Net in Base 16 — Upper bound on s
There is no (27, 129, 1443)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 219913 983373 511065 530521 393854 664426 318897 701565 967842 797097 039478 846443 596779 647470 920039 473245 141544 029813 139924 654506 107992 423948 344491 536054 838134 768896 > 16129 [i]