Best Known (67−55, 67, s)-Nets in Base 8
(67−55, 67, 48)-Net over F8 — Constructive and digital
Digital (12, 67, 48)-net over F8, using
- t-expansion [i] based on digital (11, 67, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
(67−55, 67, 49)-Net over F8 — Digital
Digital (12, 67, 49)-net over F8, using
- net from sequence [i] based on digital (12, 48)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 12 and N(F) ≥ 49, using
(67−55, 67, 214)-Net in Base 8 — Upper bound on s
There is no (12, 67, 215)-net in base 8, because
- 4 times m-reduction [i] would yield (12, 63, 215)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(863, 215, S8, 51), but
- the linear programming bound shows that M ≥ 888 049659 806526 634191 786130 362400 515913 030438 291744 086005 596735 253567 829260 820482 770094 550055 783634 864649 171965 452306 062773 016047 124480 / 1 053826 588446 508203 823694 245542 937039 065874 666654 907871 467877 113225 277242 012681 > 863 [i]
- extracting embedded orthogonal array [i] would yield OA(863, 215, S8, 51), but