Best Known (19, 19+107, s)-Nets in Base 2
(19, 19+107, 20)-Net over F2 — Constructive and digital
Digital (19, 126, 20)-net over F2, using
- net from sequence [i] based on digital (19, 19)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 19 and N(F) ≥ 20, using
(19, 19+107, 27)-Net in Base 2 — Upper bound on s
There is no (19, 126, 28)-net in base 2, because
- 23 times m-reduction [i] would yield (19, 103, 28)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2103, 28, S2, 4, 84), but
- the LP bound with quadratic polynomials shows that M ≥ 55 776626 410042 093665 854941 036544 / 5 > 2103 [i]
- extracting embedded OOA [i] would yield OOA(2103, 28, S2, 4, 84), but