Best Known (59, 59+38, s)-Nets in Base 8
(59, 59+38, 354)-Net over F8 — Constructive and digital
Digital (59, 97, 354)-net over F8, using
- 7 times m-reduction [i] based on digital (59, 104, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 52, 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, 52, 177)-net over F64, using
(59, 59+38, 384)-Net in Base 8 — Constructive
(59, 97, 384)-net in base 8, using
- 1 times m-reduction [i] based on (59, 98, 384)-net in base 8, using
- trace code for nets [i] based on (10, 49, 192)-net in base 64, using
- base change [i] based on digital (3, 42, 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, 42, 192)-net over F128, using
- trace code for nets [i] based on (10, 49, 192)-net in base 64, using
(59, 59+38, 503)-Net over F8 — Digital
Digital (59, 97, 503)-net over F8, using
(59, 59+38, 46186)-Net in Base 8 — Upper bound on s
There is no (59, 97, 46187)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 3978 651219 771636 252367 737927 426424 299661 994799 343133 420330 991250 814408 666234 231791 568352 > 897 [i]