Best Known (89, 89+74, s)-Nets in Base 2
(89, 89+74, 52)-Net over F2 — Constructive and digital
Digital (89, 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
(89, 89+74, 58)-Net over F2 — Digital
Digital (89, 163, 58)-net over F2, using
(89, 89+74, 259)-Net in Base 2 — Upper bound on s
There is no (89, 163, 260)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 12 316194 707616 637596 076793 630564 366963 524743 008256 > 2163 [i]