Best Known (99, 163, s)-Nets in Base 4
(99, 163, 130)-Net over F4 — Constructive and digital
Digital (99, 163, 130)-net over F4, using
- 23 times m-reduction [i] based on digital (99, 186, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 93, 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, 93, 65)-net over F16, using
(99, 163, 261)-Net over F4 — Digital
Digital (99, 163, 261)-net over F4, using
(99, 163, 4945)-Net in Base 4 — Upper bound on s
There is no (99, 163, 4946)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 137 095317 306111 277348 659048 501640 750497 527695 393247 747544 663205 224424 675416 173869 411119 673263 106570 > 4163 [i]