Best Known (125, 172, s)-Nets in Base 2
(125, 172, 138)-Net over F2 — Constructive and digital
Digital (125, 172, 138)-net over F2, using
- 21 times duplication [i] based on digital (124, 171, 138)-net over F2, using
- trace code for nets [i] based on digital (10, 57, 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, 57, 46)-net over F8, using
(125, 172, 197)-Net over F2 — Digital
Digital (125, 172, 197)-net over F2, using
(125, 172, 1597)-Net in Base 2 — Upper bound on s
There is no (125, 172, 1598)-net in base 2, because
- 1 times m-reduction [i] would yield (125, 171, 1598)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 3006 853689 931087 106220 851613 067214 558370 741618 830448 > 2171 [i]