Best Known (89, 89+73, s)-Nets in Base 2
(89, 89+73, 52)-Net over F2 — Constructive and digital
Digital (89, 162, 52)-net over F2, using
- t-expansion [i] based on digital (85, 162, 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
(89, 89+73, 59)-Net over F2 — Digital
Digital (89, 162, 59)-net over F2, using
(89, 89+73, 267)-Net in Base 2 — Upper bound on s
There is no (89, 162, 268)-net in base 2, because
- 1 times m-reduction [i] would yield (89, 161, 268)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 3 187740 018666 470056 355207 432257 331681 934064 740272 > 2161 [i]