Best Known (113, 151, s)-Nets in Base 4
(113, 151, 531)-Net over F4 — Constructive and digital
Digital (113, 151, 531)-net over F4, using
- 8 times m-reduction [i] based on digital (113, 159, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 53, 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, 53, 177)-net over F64, using
(113, 151, 576)-Net in Base 4 — Constructive
(113, 151, 576)-net in base 4, using
- 2 times m-reduction [i] based on (113, 153, 576)-net in base 4, using
- trace code for nets [i] based on (11, 51, 192)-net in base 64, using
- 5 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
- base change [i] based on digital (3, 48, 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, 48, 192)-net over F128, using
- 5 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
- trace code for nets [i] based on (11, 51, 192)-net in base 64, using
(113, 151, 1417)-Net over F4 — Digital
Digital (113, 151, 1417)-net over F4, using
(113, 151, 161007)-Net in Base 4 — Upper bound on s
There is no (113, 151, 161008)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 8 148855 764363 477315 557776 933741 147807 887687 099586 552692 411276 107436 503065 461881 689550 126918 > 4151 [i]