Best Known (54−45, 54, s)-Nets in Base 2
(54−45, 54, 12)-Net over F2 — Constructive and digital
Digital (9, 54, 12)-net over F2, using
- net from sequence [i] based on digital (9, 11)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 9 and N(F) ≥ 12, using
(54−45, 54, 16)-Net in Base 2 — Upper bound on s
There is no (9, 54, 17)-net in base 2, because
- 10 times m-reduction [i] would yield (9, 44, 17)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(244, 17, S2, 3, 35), but
- the LP bound with quadratic polynomials shows that M ≥ 562 949953 421312 / 27 > 244 [i]
- extracting embedded OOA [i] would yield OOA(244, 17, S2, 3, 35), but