Best Known (238−69, 238, s)-Nets in Base 2
(238−69, 238, 138)-Net over F2 — Constructive and digital
Digital (169, 238, 138)-net over F2, using
- 21 times duplication [i] based on digital (168, 237, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 79, 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, 79, 46)-net over F8, using
(238−69, 238, 225)-Net over F2 — Digital
Digital (169, 238, 225)-net over F2, using
(238−69, 238, 1647)-Net in Base 2 — Upper bound on s
There is no (169, 238, 1648)-net in base 2, because
- 1 times m-reduction [i] would yield (169, 237, 1648)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 221909 836247 642134 336515 409727 741022 837320 415482 015266 726252 395132 988803 > 2237 [i]