Best Known (182, 182+75, s)-Nets in Base 2
(182, 182+75, 138)-Net over F2 — Constructive and digital
Digital (182, 257, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (182, 258, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 86, 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
- trace code for nets [i] based on digital (10, 86, 46)-net over F8, using
(182, 182+75, 236)-Net over F2 — Digital
Digital (182, 257, 236)-net over F2, using
(182, 182+75, 1718)-Net in Base 2 — Upper bound on s
There is no (182, 257, 1719)-net in base 2, because
- 1 times m-reduction [i] would yield (182, 256, 1719)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 116300 158216 174731 876589 359175 207281 963392 052022 628121 046853 891919 660101 534340 > 2256 [i]