Best Known (6, 6+66, s)-Nets in Base 16
(6, 6+66, 65)-Net over F16 — Constructive and digital
Digital (6, 72, 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+66, 233)-Net in Base 16 — Upper bound on s
There is no (6, 72, 234)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1672, 234, S16, 66), but
- the linear programming bound shows that M ≥ 583444 061943 735225 698426 454030 516147 952930 483020 539513 036182 731618 637405 874364 140130 734558 843646 251831 060794 129422 469072 167257 971930 169344 / 1166 180758 460945 464172 372522 077419 701217 541203 155031 > 1672 [i]