Best Known (246−72, 246, s)-Nets in Base 2
(246−72, 246, 138)-Net over F2 — Constructive and digital
Digital (174, 246, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 82, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
(246−72, 246, 226)-Net over F2 — Digital
Digital (174, 246, 226)-net over F2, using
(246−72, 246, 1575)-Net in Base 2 — Upper bound on s
There is no (174, 246, 1576)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 113 718091 915301 220683 311834 690959 967989 691789 031554 045328 950750 991536 888035 > 2246 [i]