Best Known (124−90, 124, s)-Nets in Base 16
(124−90, 124, 65)-Net over F16 — Constructive and digital
Digital (34, 124, 65)-net over F16, using
- t-expansion [i] based on digital (6, 124, 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
(124−90, 124, 104)-Net in Base 16 — Constructive
(34, 124, 104)-net in base 16, using
- 1 times m-reduction [i] based on (34, 125, 104)-net in base 16, using
- base change [i] based on digital (9, 100, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- base change [i] based on digital (9, 100, 104)-net over F32, using
(124−90, 124, 193)-Net over F16 — Digital
Digital (34, 124, 193)-net over F16, using
- t-expansion [i] based on digital (33, 124, 193)-net over F16, using
- net from sequence [i] based on digital (33, 192)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 33 and N(F) ≥ 193, using
- net from sequence [i] based on digital (33, 192)-sequence over F16, using
(124−90, 124, 2419)-Net in Base 16 — Upper bound on s
There is no (34, 124, 2420)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 208132 210413 675627 826062 171630 747428 513474 748280 465696 823508 601878 400076 486112 058307 752731 381972 062713 553530 903194 981559 299458 804414 416365 594207 307876 > 16124 [i]