Best Known (77−65, 77, s)-Nets in Base 25
(77−65, 77, 126)-Net over F25 — Constructive and digital
Digital (12, 77, 126)-net over F25, using
- t-expansion [i] based on digital (10, 77, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(77−65, 77, 1096)-Net in Base 25 — Upper bound on s
There is no (12, 77, 1097)-net in base 25, because
- 1 times m-reduction [i] would yield (12, 76, 1097)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 17543 585306 150597 063510 749569 614175 900188 067228 018104 351931 926234 613457 750136 658656 404030 305790 771179 243265 > 2576 [i]