Best Known (6, 6+65, s)-Nets in Base 16
(6, 6+65, 65)-Net over F16 — Constructive and digital
Digital (6, 71, 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+65, 235)-Net in Base 16 — Upper bound on s
There is no (6, 71, 236)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1671, 236, S16, 65), but
- the linear programming bound shows that M ≥ 6589 244238 144147 416424 802426 321141 034494 978516 499423 661462 466906 314508 354140 653961 567979 739761 697719 323953 777522 187201 890846 790894 396836 413440 / 206 391875 124792 353545 227690 933099 351272 639960 802216 067619 > 1671 [i]