Best Known (121, 121+44, s)-Nets in Base 4
(121, 121+44, 531)-Net over F4 — Constructive and digital
Digital (121, 165, 531)-net over F4, using
- 6 times m-reduction [i] based on digital (121, 171, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 57, 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, 57, 177)-net over F64, using
(121, 121+44, 576)-Net in Base 4 — Constructive
(121, 165, 576)-net in base 4, using
- trace code for nets [i] based on (11, 55, 192)-net in base 64, using
- 1 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
- 1 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
(121, 121+44, 1171)-Net over F4 — Digital
Digital (121, 165, 1171)-net over F4, using
(121, 121+44, 98878)-Net in Base 4 — Upper bound on s
There is no (121, 165, 98879)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2187 325308 747621 035540 067215 399844 173012 893521 482714 224693 515604 507494 144927 703541 650495 016867 644315 > 4165 [i]