Best Known (117−40, 117, s)-Nets in Base 4
(117−40, 117, 147)-Net over F4 — Constructive and digital
Digital (77, 117, 147)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 25, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (52, 92, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 46, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 46, 65)-net over F16, using
- digital (5, 25, 17)-net over F4, using
(117−40, 117, 152)-Net in Base 4 — Constructive
(77, 117, 152)-net in base 4, using
- 3 times m-reduction [i] based on (77, 120, 152)-net in base 4, using
- trace code for nets [i] based on (17, 60, 76)-net in base 16, using
- base change [i] based on digital (5, 48, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- base change [i] based on digital (5, 48, 76)-net over F32, using
- trace code for nets [i] based on (17, 60, 76)-net in base 16, using
(117−40, 117, 320)-Net over F4 — Digital
Digital (77, 117, 320)-net over F4, using
(117−40, 117, 9193)-Net in Base 4 — Upper bound on s
There is no (77, 117, 9194)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 27646 485002 875142 797542 012448 268667 159421 424978 796400 667366 942822 573884 > 4117 [i]