Best Known (108, 173, s)-Nets in Base 8
(108, 173, 354)-Net over F8 — Constructive and digital
Digital (108, 173, 354)-net over F8, using
- 81 times duplication [i] based on digital (107, 172, 354)-net over F8, using
- t-expansion [i] based on digital (93, 172, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 86, 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, 86, 177)-net over F64, using
- t-expansion [i] based on digital (93, 172, 354)-net over F8, using
(108, 173, 432)-Net in Base 8 — Constructive
(108, 173, 432)-net in base 8, using
- 81 times duplication [i] based on (107, 172, 432)-net in base 8, using
- t-expansion [i] based on (104, 172, 432)-net in base 8, using
- trace code for nets [i] based on (18, 86, 216)-net in base 64, using
- 5 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- base change [i] based on digital (5, 78, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 78, 216)-net over F128, using
- 5 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- trace code for nets [i] based on (18, 86, 216)-net in base 64, using
- t-expansion [i] based on (104, 172, 432)-net in base 8, using
(108, 173, 980)-Net over F8 — Digital
Digital (108, 173, 980)-net over F8, using
(108, 173, 130564)-Net in Base 8 — Upper bound on s
There is no (108, 173, 130565)-net in base 8, because
- 1 times m-reduction [i] would yield (108, 172, 130565)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 214564 773687 092927 535392 590482 007138 257788 374855 420443 411115 119706 595922 609644 438234 635754 647737 288153 912501 670998 611999 595943 693611 650497 122240 754748 757904 > 8172 [i]