Best Known (258−181, 258, s)-Nets in Base 2
(258−181, 258, 50)-Net over F2 — Constructive and digital
Digital (77, 258, 50)-net over F2, using
- t-expansion [i] based on digital (75, 258, 50)-net over F2, using
- net from sequence [i] based on digital (75, 49)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (75, 49)-sequence over F2, using
(258−181, 258, 52)-Net over F2 — Digital
Digital (77, 258, 52)-net over F2, using
- net from sequence [i] based on digital (77, 51)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 77 and N(F) ≥ 52, using
(258−181, 258, 112)-Net in Base 2 — Upper bound on s
There is no (77, 258, 113)-net in base 2, because
- 40 times m-reduction [i] would yield (77, 218, 113)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2218, 113, S2, 2, 141), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 40 439920 000725 959692 000522 630529 446010 455716 633810 858721 655415 373824 / 71 > 2218 [i]
- extracting embedded OOA [i] would yield OOA(2218, 113, S2, 2, 141), but