Best Known (62, 62+∞, s)-Nets in Base 2
(62, 62+∞, 43)-Net over F2 — Constructive and digital
Digital (62, m, 43)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (62, 42)-sequence over F2, using
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- t-expansion [i] based on digital (59, 42)-sequence over F2, using
(62, 62+∞, 44)-Net over F2 — Digital
Digital (62, m, 44)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (62, 43)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 62 and N(F) ≥ 44, using
(62, 62+∞, 71)-Net in Base 2 — Upper bound on s
There is no (62, m, 72)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (62, 423, 72)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2423, 72, S2, 6, 361), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4852 171964 711426 004262 224822 250396 481013 764881 907679 006548 339266 075587 288659 844840 319955 210682 244261 670434 619182 456250 700704 776192 / 181 > 2423 [i]
- extracting embedded OOA [i] would yield OOA(2423, 72, S2, 6, 361), but