Best Known (163−75, 163, s)-Nets in Base 2
(163−75, 163, 52)-Net over F2 — Constructive and digital
Digital (88, 163, 52)-net over F2, using
- t-expansion [i] based on digital (85, 163, 52)-net over F2, using
- net from sequence [i] based on digital (85, 51)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 3 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (85, 51)-sequence over F2, using
(163−75, 163, 57)-Net over F2 — Digital
Digital (88, 163, 57)-net over F2, using
- t-expansion [i] based on digital (83, 163, 57)-net over F2, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 83 and N(F) ≥ 57, using
- net from sequence [i] based on digital (83, 56)-sequence over F2, using
(163−75, 163, 253)-Net in Base 2 — Upper bound on s
There is no (88, 163, 254)-net in base 2, because
- 1 times m-reduction [i] would yield (88, 162, 254)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 5 936015 882385 584718 037808 648426 776891 915436 610297 > 2162 [i]