Best Known (7, 7+71, s)-Nets in Base 16
(7, 7+71, 65)-Net over F16 — Constructive and digital
Digital (7, 78, 65)-net over F16, using
- t-expansion [i] based on digital (6, 78, 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
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(7, 7+71, 281)-Net in Base 16 — Upper bound on s
There is no (7, 78, 282)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1678, 282, S16, 71), but
- the linear programming bound shows that M ≥ 6 606718 883264 289538 399533 883845 708613 399509 471683 845616 345400 558079 611592 560996 174039 917039 601574 093316 187592 847845 755834 308616 762993 633302 985700 573551 001600 / 770 170750 151456 739914 211650 781645 222579 844141 705823 657904 450739 > 1678 [i]