Best Known (99−71, 99, s)-Nets in Base 2
(99−71, 99, 21)-Net over F2 — Constructive and digital
Digital (28, 99, 21)-net over F2, using
- t-expansion [i] based on digital (21, 99, 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
(99−71, 99, 25)-Net over F2 — Digital
Digital (28, 99, 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
(99−71, 99, 45)-Net in Base 2 — Upper bound on s
There is no (28, 99, 46)-net in base 2, because
- 14 times m-reduction [i] would yield (28, 85, 46)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(285, 46, S2, 2, 57), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1237 940039 285380 274899 124224 / 29 > 285 [i]
- extracting embedded OOA [i] would yield OOA(285, 46, S2, 2, 57), but