Best Known (131, 198, s)-Nets in Base 3
(131, 198, 162)-Net over F3 — Constructive and digital
Digital (131, 198, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 99, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
(131, 198, 301)-Net over F3 — Digital
Digital (131, 198, 301)-net over F3, using
(131, 198, 4608)-Net in Base 3 — Upper bound on s
There is no (131, 198, 4609)-net in base 3, because
- 1 times m-reduction [i] would yield (131, 197, 4609)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 9879 556274 870765 707794 199680 198970 967428 633958 516835 038378 444925 244935 291866 896477 483417 886595 > 3197 [i]