Best Known (258−144, 258, s)-Nets in Base 2
(258−144, 258, 57)-Net over F2 — Constructive and digital
Digital (114, 258, 57)-net over F2, using
- t-expansion [i] based on digital (110, 258, 57)-net over F2, using
- net from sequence [i] based on digital (110, 56)-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 8 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 (110, 56)-sequence over F2, using
(258−144, 258, 73)-Net over F2 — Digital
Digital (114, 258, 73)-net over F2, using
- net from sequence [i] based on digital (114, 72)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 114 and N(F) ≥ 73, using
(258−144, 258, 237)-Net in Base 2 — Upper bound on s
There is no (114, 258, 238)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 532571 942678 905170 793142 494401 960551 590742 674323 994465 295217 344961 022910 526787 > 2258 [i]