Best Known (6, 6+55, s)-Nets in Base 16
(6, 6+55, 65)-Net over F16 — Constructive and digital
Digital (6, 61, 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
(6, 6+55, 270)-Net in Base 16 — Upper bound on s
There is no (6, 61, 271)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1661, 271, S16, 55), but
- the linear programming bound shows that M ≥ 258 111880 706791 883549 426712 581108 417332 589403 736457 703899 527320 034754 992942 300344 831637 519278 608250 539114 649839 641500 319744 / 8 790622 858248 169329 454264 365828 222744 514823 941159 > 1661 [i]