Best Known (153, 209, s)-Nets in Base 4
(153, 209, 531)-Net over F4 — Constructive and digital
Digital (153, 209, 531)-net over F4, using
- 10 times m-reduction [i] based on digital (153, 219, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 73, 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, 73, 177)-net over F64, using
(153, 209, 576)-Net in Base 4 — Constructive
(153, 209, 576)-net in base 4, using
- 1 times m-reduction [i] based on (153, 210, 576)-net in base 4, using
- trace code for nets [i] based on (13, 70, 192)-net in base 64, using
- base change [i] based on digital (3, 60, 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, 60, 192)-net over F128, using
- trace code for nets [i] based on (13, 70, 192)-net in base 64, using
(153, 209, 1407)-Net over F4 — Digital
Digital (153, 209, 1407)-net over F4, using
(153, 209, 117421)-Net in Base 4 — Upper bound on s
There is no (153, 209, 117422)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 677023 555037 155929 736780 487527 810223 929217 347235 068875 598854 942723 935534 265808 092597 884245 731694 223356 022205 736516 575864 393466 > 4209 [i]