Best Known (172, 172+47, s)-Nets in Base 2
(172, 172+47, 260)-Net over F2 — Constructive and digital
Digital (172, 219, 260)-net over F2, using
- t-expansion [i] based on digital (171, 219, 260)-net over F2, using
- 1 times m-reduction [i] based on digital (171, 220, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 55, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 55, 65)-net over F16, using
- 1 times m-reduction [i] based on digital (171, 220, 260)-net over F2, using
(172, 172+47, 454)-Net over F2 — Digital
Digital (172, 219, 454)-net over F2, using
(172, 172+47, 6691)-Net in Base 2 — Upper bound on s
There is no (172, 219, 6692)-net in base 2, because
- 1 times m-reduction [i] would yield (172, 218, 6692)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 422471 272573 730924 873623 645218 851004 722676 746104 255214 592556 099080 > 2218 [i]