Best Known (33−32, 33, s)-Nets in Base 16
(33−32, 33, 24)-Net over F16 — Constructive and digital
Digital (1, 33, 24)-net over F16, using
- net from sequence [i] based on digital (1, 23)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
(33−32, 33, 25)-Net over F16 — Digital
Digital (1, 33, 25)-net over F16, using
- net from sequence [i] based on digital (1, 24)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 25, using
(33−32, 33, 33)-Net over F16 — Upper bound on s (digital)
There is no digital (1, 33, 34)-net over F16, because
- 2 times m-reduction [i] would yield digital (1, 31, 34)-net over F16, but
- extracting embedded orthogonal array [i] would yield linear OA(1631, 34, F16, 30) (dual of [34, 3, 31]-code), but
(33−32, 33, 34)-Net in Base 16 — Upper bound on s
There is no (1, 33, 35)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1633, 35, S16, 32), but
- the (dual) Plotkin bound shows that M ≥ 87112 285931 760246 646623 899502 532662 132736 / 11 > 1633 [i]