Best Known (219−186, 219, s)-Nets in Base 2
(219−186, 219, 24)-Net over F2 — Constructive and digital
Digital (33, 219, 24)-net over F2, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
(219−186, 219, 28)-Net over F2 — Digital
Digital (33, 219, 28)-net over F2, using
- net from sequence [i] based on digital (33, 27)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 28, using
(219−186, 219, 41)-Net in Base 2 — Upper bound on s
There is no (33, 219, 42)-net in base 2, because
- 17 times m-reduction [i] would yield (33, 202, 42)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2202, 42, S2, 5, 169), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 565 642191 579164 576990 770656 504089 236087 815453 811543 078026 084352 / 85 > 2202 [i]
- extracting embedded OOA [i] would yield OOA(2202, 42, S2, 5, 169), but