Best Known (111−105, 111, s)-Nets in Base 16
(111−105, 111, 65)-Net over F16 — Constructive and digital
Digital (6, 111, 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
(111−105, 111, 106)-Net in Base 16 — Upper bound on s
There is no (6, 111, 107)-net in base 16, because
- 15 times m-reduction [i] would yield (6, 96, 107)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(1696, 107, S16, 90), but
- the linear programming bound shows that M ≥ 632381 165715 575607 270607 577961 002582 507033 932404 234102 073968 038308 365606 364351 282586 241545 781633 648349 739341 287044 099254 255616 / 15885 182313 > 1696 [i]
- extracting embedded orthogonal array [i] would yield OA(1696, 107, S16, 90), but