Best Known (6, 6+61, s)-Nets in Base 16
(6, 6+61, 65)-Net over F16 — Constructive and digital
Digital (6, 67, 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+61, 257)-Net in Base 16 — Upper bound on s
There is no (6, 67, 258)-net in base 16, because
- 1 times m-reduction [i] would yield (6, 66, 258)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(1666, 258, S16, 60), but
- the linear programming bound shows that M ≥ 1 831068 329807 427886 693930 243021 843563 706420 919135 055008 442822 474518 284634 946184 791199 617279 638968 444720 313679 042286 103266 590720 / 61227 472926 450174 211522 981063 856899 560129 492773 > 1666 [i]
- extracting embedded orthogonal array [i] would yield OA(1666, 258, S16, 60), but