Best Known (106−49, 106, s)-Nets in Base 2
(106−49, 106, 42)-Net over F2 — Constructive and digital
Digital (57, 106, 42)-net over F2, using
- t-expansion [i] based on digital (54, 106, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
(106−49, 106, 144)-Net in Base 2 — Upper bound on s
There is no (57, 106, 145)-net in base 2, because
- 1 times m-reduction [i] would yield (57, 105, 145)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2105, 145, S2, 48), but
- the linear programming bound shows that M ≥ 727 070369 678229 731686 401086 929362 121333 407744 / 17 521374 765895 > 2105 [i]
- extracting embedded orthogonal array [i] would yield OA(2105, 145, S2, 48), but