Best Known (56, 56+44, s)-Nets in Base 32
(56, 56+44, 272)-Net over F32 — Constructive and digital
Digital (56, 100, 272)-net over F32, using
- 1 times m-reduction [i] based on digital (56, 101, 272)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (5, 20, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- digital (7, 29, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (7, 52, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (5, 20, 76)-net over F32, using
- generalized (u, u+v)-construction [i] based on
(56, 56+44, 513)-Net in Base 32 — Constructive
(56, 100, 513)-net in base 32, using
- t-expansion [i] based on (46, 100, 513)-net in base 32, using
- 8 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- base change [i] based on digital (28, 90, 513)-net over F64, using
- 8 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(56, 56+44, 1745)-Net over F32 — Digital
Digital (56, 100, 1745)-net over F32, using
(56, 56+44, 2028055)-Net in Base 32 — Upper bound on s
There is no (56, 100, 2028056)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 3 273423 718248 137784 409048 492465 267078 508915 365410 735971 974625 366475 772304 540646 093456 146996 223180 797211 813348 067924 439482 013787 710495 874970 471622 262327 > 32100 [i]