Best Known (128−95, 128, s)-Nets in Base 16
(128−95, 128, 65)-Net over F16 — Constructive and digital
Digital (33, 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
(128−95, 128, 98)-Net in Base 16 — Constructive
(33, 128, 98)-net in base 16, using
- 2 times m-reduction [i] based on (33, 130, 98)-net in base 16, using
- base change [i] based on digital (7, 104, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- base change [i] based on digital (7, 104, 98)-net over F32, using
(128−95, 128, 193)-Net over F16 — Digital
Digital (33, 128, 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
(128−95, 128, 2170)-Net in Base 16 — Upper bound on s
There is no (33, 128, 2171)-net in base 16, because
- 1 times m-reduction [i] would yield (33, 127, 2171)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 851 454492 103634 764542 614174 573363 917583 720867 505129 532329 462132 200321 311231 265691 201564 528096 324029 404284 439040 611846 351644 404461 039297 414968 179334 788656 > 16127 [i]