Best Known (163−44, 163, s)-Nets in Base 2
(163−44, 163, 138)-Net over F2 — Constructive and digital
Digital (119, 163, 138)-net over F2, using
- 21 times duplication [i] based on digital (118, 162, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 54, 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, 54, 46)-net over F8, using
(163−44, 163, 194)-Net over F2 — Digital
Digital (119, 163, 194)-net over F2, using
(163−44, 163, 1506)-Net in Base 2 — Upper bound on s
There is no (119, 163, 1507)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 11 739948 422280 336468 087140 378004 494046 632334 439464 > 2163 [i]