Best Known (164, 231, s)-Nets in Base 2
(164, 231, 138)-Net over F2 — Constructive and digital
Digital (164, 231, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 77, 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
(164, 231, 219)-Net over F2 — Digital
Digital (164, 231, 219)-net over F2, using
(164, 231, 1601)-Net in Base 2 — Upper bound on s
There is no (164, 231, 1602)-net in base 2, because
- 1 times m-reduction [i] would yield (164, 230, 1602)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1742 910171 972451 076656 163334 894479 008412 949720 476238 704423 928676 723330 > 2230 [i]