Best Known (250−161, 250, s)-Nets in Base 2
(250−161, 250, 52)-Net over F2 — Constructive and digital
Digital (89, 250, 52)-net over F2, using
- t-expansion [i] based on digital (85, 250, 52)-net over F2, using
- net from sequence [i] based on digital (85, 51)-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 3 places 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 (85, 51)-sequence over F2, using
(250−161, 250, 57)-Net over F2 — Digital
Digital (89, 250, 57)-net over F2, using
- t-expansion [i] based on digital (83, 250, 57)-net over F2, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 83 and N(F) ≥ 57, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
(250−161, 250, 128)-Net in Base 2 — Upper bound on s
There is no (89, 250, 129)-net in base 2, because
- extracting embedded OOA [i] would yield OOA(2250, 129, S2, 2, 161), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 57896 044618 658097 711785 492504 343953 926634 992332 820282 019728 792003 956564 819968 / 27 > 2250 [i]