Best Known (258−174, 258, s)-Nets in Base 2
(258−174, 258, 51)-Net over F2 — Constructive and digital
Digital (84, 258, 51)-net over F2, using
- t-expansion [i] based on digital (80, 258, 51)-net over F2, using
- net from sequence [i] based on digital (80, 50)-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 2 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 (80, 50)-sequence over F2, using
(258−174, 258, 57)-Net over F2 — Digital
Digital (84, 258, 57)-net over F2, using
- t-expansion [i] based on digital (83, 258, 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
(258−174, 258, 121)-Net in Base 2 — Upper bound on s
There is no (84, 258, 122)-net in base 2, because
- 21 times m-reduction [i] would yield (84, 237, 122)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2237, 122, S2, 2, 153), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 21 202164 777340 611954 999570 008915 022189 929806 762507 427497 459274 415511 437312 / 77 > 2237 [i]
- extracting embedded OOA [i] would yield OOA(2237, 122, S2, 2, 153), but