Best Known (253−74, 253, s)-Nets in Base 2
(253−74, 253, 138)-Net over F2 — Constructive and digital
Digital (179, 253, 138)-net over F2, using
- 21 times duplication [i] based on digital (178, 252, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 84, 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, 84, 46)-net over F8, using
(253−74, 253, 232)-Net over F2 — Digital
Digital (179, 253, 232)-net over F2, using
(253−74, 253, 1621)-Net in Base 2 — Upper bound on s
There is no (179, 253, 1622)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 14494 331668 929382 179022 890600 068073 639316 333879 867077 238675 148910 576821 577438 > 2253 [i]