Best Known (67−51, 67, s)-Nets in Base 128
(67−51, 67, 288)-Net over F128 — Constructive and digital
Digital (16, 67, 288)-net over F128, using
- t-expansion [i] based on digital (9, 67, 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
(67−51, 67, 386)-Net over F128 — Digital
Digital (16, 67, 386)-net over F128, using
- t-expansion [i] based on digital (15, 67, 386)-net over F128, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
(67−51, 67, 29287)-Net in Base 128 — Upper bound on s
There is no (16, 67, 29288)-net in base 128, because
- 1 times m-reduction [i] would yield (16, 66, 29288)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 11 918193 695146 336304 639080 014150 298903 683632 827826 446471 539642 019413 470741 492112 405855 694496 670765 184677 193340 051623 397516 526292 514045 979180 > 12866 [i]