Best Known (77−71, 77, s)-Nets in Base 16
(77−71, 77, 65)-Net over F16 — Constructive and digital
Digital (6, 77, 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
(77−71, 77, 217)-Net in Base 16 — Upper bound on s
There is no (6, 77, 218)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1677, 218, S16, 71), but
- the linear programming bound shows that M ≥ 39239 300541 219540 329631 913169 651885 660254 163645 739597 686079 493504 901520 307057 626216 121457 409040 843419 733043 481143 719277 630469 836998 945975 243496 196482 793472 / 74 804260 047677 894682 341794 388879 812831 718081 992873 708278 167107 > 1677 [i]