Best Known (96, 96+48, s)-Nets in Base 8
(96, 96+48, 400)-Net over F8 — Constructive and digital
Digital (96, 144, 400)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (10, 34, 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 (62, 110, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 55, 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, 55, 177)-net over F64, using
- digital (10, 34, 46)-net over F8, using
(96, 96+48, 576)-Net in Base 8 — Constructive
(96, 144, 576)-net in base 8, using
- 8 times m-reduction [i] based on (96, 152, 576)-net in base 8, using
- trace code for nets [i] based on (20, 76, 288)-net in base 64, using
- 1 times m-reduction [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
- 1 times m-reduction [i] based on (20, 77, 288)-net in base 64, using
- trace code for nets [i] based on (20, 76, 288)-net in base 64, using
(96, 96+48, 1558)-Net over F8 — Digital
Digital (96, 144, 1558)-net over F8, using
(96, 96+48, 367102)-Net in Base 8 — Upper bound on s
There is no (96, 144, 367103)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 11091 276860 840745 870524 409196 623875 983665 636359 715209 696575 425731 848443 247559 285018 047042 458673 477898 482270 157385 316635 664798 483769 > 8144 [i]