Best Known (125−117, 125, s)-Nets in Base 16
(125−117, 125, 65)-Net over F16 — Constructive and digital
Digital (8, 125, 65)-net over F16, using
- t-expansion [i] based on digital (6, 125, 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
(125−117, 125, 161)-Net in Base 16 — Upper bound on s
There is no (8, 125, 162)-net in base 16, because
- 7 times m-reduction [i] would yield (8, 118, 162)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(16118, 162, S16, 110), but
- the linear programming bound shows that M ≥ 67094 250143 496863 765945 730599 677506 281097 054797 487214 706877 103483 276101 353471 276226 918006 219975 937180 683388 806856 799132 700635 802263 722925 587419 834381 300386 510535 149825 818624 / 5 332004 745796 121301 490270 732015 > 16118 [i]
- extracting embedded orthogonal array [i] would yield OA(16118, 162, S16, 110), but