Best Known (193−165, 193, s)-Nets in Base 2
(193−165, 193, 21)-Net over F2 — Constructive and digital
Digital (28, 193, 21)-net over F2, using
- t-expansion [i] based on digital (21, 193, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
(193−165, 193, 25)-Net over F2 — Digital
Digital (28, 193, 25)-net over F2, using
- net from sequence [i] based on digital (28, 24)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 28 and N(F) ≥ 25, using
(193−165, 193, 36)-Net in Base 2 — Upper bound on s
There is no (28, 193, 37)-net in base 2, because
- 17 times m-reduction [i] would yield (28, 176, 37)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2176, 37, S2, 5, 148), but
- the LP bound with quadratic polynomials shows that M ≥ 14 750269 580834 180261 699090 136321 725892 330364 051017 170944 / 149 > 2176 [i]
- extracting embedded OOA [i] would yield OOA(2176, 37, S2, 5, 148), but