Best Known (77−65, 77, s)-Nets in Base 128
(77−65, 77, 288)-Net over F128 — Constructive and digital
Digital (12, 77, 288)-net over F128, using
- t-expansion [i] based on digital (9, 77, 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
(77−65, 77, 321)-Net over F128 — Digital
Digital (12, 77, 321)-net over F128, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 12 and N(F) ≥ 321, using
(77−65, 77, 10163)-Net in Base 128 — Upper bound on s
There is no (12, 77, 10164)-net in base 128, because
- 1 times m-reduction [i] would yield (12, 76, 10164)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 14097 151486 007305 794624 830120 908071 535698 616026 322190 916990 167418 394329 425720 027188 938811 130551 961025 730576 857784 320690 811538 500820 916602 269276 809428 736990 870555 > 12876 [i]