Best Known (113−44, 113, s)-Nets in Base 8
(113−44, 113, 354)-Net over F8 — Constructive and digital
Digital (69, 113, 354)-net over F8, using
- 11 times m-reduction [i] based on digital (69, 124, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 62, 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, 62, 177)-net over F64, using
(113−44, 113, 384)-Net in Base 8 — Constructive
(69, 113, 384)-net in base 8, using
- 81 times duplication [i] based on (68, 112, 384)-net in base 8, using
- t-expansion [i] based on (67, 112, 384)-net in base 8, using
- trace code for nets [i] based on (11, 56, 192)-net in base 64, using
- base change [i] based on digital (3, 48, 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, 48, 192)-net over F128, using
- trace code for nets [i] based on (11, 56, 192)-net in base 64, using
- t-expansion [i] based on (67, 112, 384)-net in base 8, using
(113−44, 113, 581)-Net over F8 — Digital
Digital (69, 113, 581)-net over F8, using
(113−44, 113, 56266)-Net in Base 8 — Upper bound on s
There is no (69, 113, 56267)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 1 120183 577593 148862 973530 043769 392315 770514 453476 134137 581849 978230 104480 185573 809861 843643 509953 659528 > 8113 [i]