Best Known (106, 106+38, s)-Nets in Base 2
(106, 106+38, 138)-Net over F2 — Constructive and digital
Digital (106, 144, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 48, 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
(106, 106+38, 187)-Net over F2 — Digital
Digital (106, 144, 187)-net over F2, using
(106, 106+38, 1488)-Net in Base 2 — Upper bound on s
There is no (106, 144, 1489)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 22 509432 848035 619605 136206 042496 617241 699816 > 2144 [i]