Best Known (6, 6+56, s)-Nets in Base 16
(6, 6+56, 65)-Net over F16 — Constructive and digital
Digital (6, 62, 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+56, 264)-Net in Base 16 — Upper bound on s
There is no (6, 62, 265)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1662, 265, S16, 56), but
- the linear programming bound shows that M ≥ 4 515221 802877 362901 794033 285693 493809 004743 687965 602568 816003 327551 122069 428167 594487 347892 377266 796367 393516 735692 800000 / 9868 571477 470768 055900 180053 268858 124294 149629 > 1662 [i]