Best Known (84, 84+118, s)-Nets in Base 2
(84, 84+118, 51)-Net over F2 — Constructive and digital
Digital (84, 202, 51)-net over F2, using
- t-expansion [i] based on digital (80, 202, 51)-net over F2, using
- net from sequence [i] based on digital (80, 50)-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 2 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 (80, 50)-sequence over F2, using
(84, 84+118, 57)-Net over F2 — Digital
Digital (84, 202, 57)-net over F2, using
- t-expansion [i] based on digital (83, 202, 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
(84, 84+118, 169)-Net in Base 2 — Upper bound on s
There is no (84, 202, 170)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 8 148193 021974 804309 675179 528359 910098 060011 630314 347678 910240 > 2202 [i]