Best Known (149−50, 149, s)-Nets in Base 8
(149−50, 149, 400)-Net over F8 — Constructive and digital
Digital (99, 149, 400)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (10, 35, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- digital (64, 114, 354)-net over F8, 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
- digital (10, 35, 46)-net over F8, using
(149−50, 149, 576)-Net in Base 8 — Constructive
(99, 149, 576)-net in base 8, using
- t-expansion [i] based on (97, 149, 576)-net in base 8, using
- 5 times m-reduction [i] based on (97, 154, 576)-net in base 8, using
- trace code for nets [i] based on (20, 77, 288)-net in base 64, using
- base change [i] based on digital (9, 66, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 66, 288)-net over F128, using
- trace code for nets [i] based on (20, 77, 288)-net in base 64, using
- 5 times m-reduction [i] based on (97, 154, 576)-net in base 8, using
(149−50, 149, 1546)-Net over F8 — Digital
Digital (99, 149, 1546)-net over F8, using
(149−50, 149, 350691)-Net in Base 8 — Upper bound on s
There is no (99, 149, 350692)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 363 440954 296734 072251 958566 217521 761782 818294 428764 306050 020320 547655 569837 764772 952202 911915 786439 003723 981883 654905 992663 044986 812692 > 8149 [i]