Best Known (81−74, 81, s)-Nets in Base 16
(81−74, 81, 65)-Net over F16 — Constructive and digital
Digital (7, 81, 65)-net over F16, using
- t-expansion [i] based on digital (6, 81, 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
(81−74, 81, 265)-Net in Base 16 — Upper bound on s
There is no (7, 81, 266)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1681, 266, S16, 74), but
- the linear programming bound shows that M ≥ 380 329038 376734 664246 865876 094127 455596 817310 268019 095801 649165 222342 129149 300048 574451 370461 146633 156351 023738 426962 132347 532081 357471 838142 763339 601473 913666 369539 276800 / 10 889618 686073 542752 335368 221950 484649 177257 047590 355195 649378 129467 432831 > 1681 [i]