Best Known (63, 258, s)-Nets in Base 2
(63, 258, 43)-Net over F2 — Constructive and digital
Digital (63, 258, 43)-net over F2, using
- t-expansion [i] based on digital (59, 258, 43)-net over F2, using
- net from sequence [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]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
(63, 258, 44)-Net over F2 — Digital
Digital (63, 258, 44)-net over F2, using
- t-expansion [i] based on digital (62, 258, 44)-net over F2, 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
- net from sequence [i] based on digital (62, 43)-sequence over F2, using
(63, 258, 80)-Net in Base 2 — Upper bound on s
There is no (63, 258, 81)-net in base 2, because
- 23 times m-reduction [i] would yield (63, 235, 81)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2235, 81, S2, 3, 172), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 12 367929 453448 690307 083082 505200 429610 792387 278129 332706 851243 409048 338432 / 173 > 2235 [i]
- extracting embedded OOA [i] would yield OOA(2235, 81, S2, 3, 172), but