Best Known (252−196, 252, s)-Nets in Base 2
(252−196, 252, 42)-Net over F2 — Constructive and digital
Digital (56, 252, 42)-net over F2, using
- t-expansion [i] based on digital (54, 252, 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
(252−196, 252, 72)-Net in Base 2 — Upper bound on s
There is no (56, 252, 73)-net in base 2, because
- 42 times m-reduction [i] would yield (56, 210, 73)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2210, 73, S2, 3, 154), but
- the LP bound with quadratic polynomials shows that M ≥ 842498 333348 457493 583344 221469 363458 551160 763204 392890 034487 820288 / 465 > 2210 [i]
- extracting embedded OOA [i] would yield OOA(2210, 73, S2, 3, 154), but