Best Known (135−34, 135, s)-Nets in Base 4
(135−34, 135, 531)-Net over F4 — Constructive and digital
Digital (101, 135, 531)-net over F4, using
- 6 times m-reduction [i] based on digital (101, 141, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 47, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 47, 177)-net over F64, using
(135−34, 135, 576)-Net in Base 4 — Constructive
(101, 135, 576)-net in base 4, using
- t-expansion [i] based on (100, 135, 576)-net in base 4, using
- trace code for nets [i] based on (10, 45, 192)-net in base 64, using
- 4 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
- base change [i] based on digital (3, 42, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 42, 192)-net over F128, using
- 4 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
- trace code for nets [i] based on (10, 45, 192)-net in base 64, using
(135−34, 135, 1290)-Net over F4 — Digital
Digital (101, 135, 1290)-net over F4, using
(135−34, 135, 144493)-Net in Base 4 — Upper bound on s
There is no (101, 135, 144494)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1897 308254 769733 489004 586323 201216 418074 444878 075474 093401 736083 469733 013961 537930 > 4135 [i]