Best Known (125−31, 125, s)-Nets in Base 2
(125−31, 125, 138)-Net over F2 — Constructive and digital
Digital (94, 125, 138)-net over F2, using
- 1 times m-reduction [i] based on digital (94, 126, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 42, 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
- trace code for nets [i] based on digital (10, 42, 46)-net over F8, using
(125−31, 125, 195)-Net over F2 — Digital
Digital (94, 125, 195)-net over F2, using
(125−31, 125, 1956)-Net in Base 2 — Upper bound on s
There is no (94, 125, 1957)-net in base 2, because
- 1 times m-reduction [i] would yield (94, 124, 1957)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 21 370993 611095 112684 006287 933834 832480 > 2124 [i]