Best Known (123, 123+42, s)-Nets in Base 4
(123, 123+42, 531)-Net over F4 — Constructive and digital
Digital (123, 165, 531)-net over F4, using
- 9 times m-reduction [i] based on digital (123, 174, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 58, 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, 58, 177)-net over F64, using
(123, 123+42, 648)-Net in Base 4 — Constructive
(123, 165, 648)-net in base 4, using
- trace code for nets [i] based on (13, 55, 216)-net in base 64, using
- 1 times m-reduction [i] based on (13, 56, 216)-net in base 64, using
- base change [i] based on digital (5, 48, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 48, 216)-net over F128, using
- 1 times m-reduction [i] based on (13, 56, 216)-net in base 64, using
(123, 123+42, 1445)-Net over F4 — Digital
Digital (123, 165, 1445)-net over F4, using
(123, 123+42, 155523)-Net in Base 4 — Upper bound on s
There is no (123, 165, 155524)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2187 484668 445566 919774 428117 172816 986282 896298 512991 092417 962728 177862 908502 083800 763510 642532 385248 > 4165 [i]