Best Known (80−74, 80, s)-Nets in Base 16
(80−74, 80, 65)-Net over F16 — Constructive and digital
Digital (6, 80, 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
(80−74, 80, 206)-Net in Base 16 — Upper bound on s
There is no (6, 80, 207)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1680, 207, S16, 74), but
- the linear programming bound shows that M ≥ 94197 449956 626298 355837 380115 973123 578618 168165 814221 333332 062184 072034 634892 376916 750200 592917 325017 914556 695985 146514 289835 980145 986346 418176 / 42910 252362 250417 304370 380368 901690 649842 343127 > 1680 [i]