Best Known (59−53, 59, s)-Nets in Base 81
(59−53, 59, 160)-Net over F81 — Constructive and digital
Digital (6, 59, 160)-net over F81, using
- t-expansion [i] based on digital (5, 59, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
(59−53, 59, 190)-Net over F81 — Digital
Digital (6, 59, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
(59−53, 59, 2372)-Net in Base 81 — Upper bound on s
There is no (6, 59, 2373)-net in base 81, because
- 1 times m-reduction [i] would yield (6, 58, 2373)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 493 469052 975643 275320 406360 663011 078100 606310 706649 483950 329322 657736 398762 052929 611443 396999 240507 452447 015841 > 8158 [i]