Best Known (117, 117+40, s)-Nets in Base 4
(117, 117+40, 531)-Net over F4 — Constructive and digital
Digital (117, 157, 531)-net over F4, using
- 8 times m-reduction [i] based on digital (117, 165, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 55, 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, 55, 177)-net over F64, using
(117, 117+40, 576)-Net in Base 4 — Constructive
(117, 157, 576)-net in base 4, using
- 2 times m-reduction [i] based on (117, 159, 576)-net in base 4, using
- trace code for nets [i] based on (11, 53, 192)-net in base 64, using
- 3 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
- 3 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
- trace code for nets [i] based on (11, 53, 192)-net in base 64, using
(117, 117+40, 1381)-Net over F4 — Digital
Digital (117, 157, 1381)-net over F4, using
(117, 117+40, 147335)-Net in Base 4 — Upper bound on s
There is no (117, 157, 147336)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 33375 744266 939419 677189 062123 732142 757979 459921 977760 323425 071304 965313 100481 727314 112566 299576 > 4157 [i]