Best Known (127, 190, s)-Nets in Base 3
(127, 190, 162)-Net over F3 — Constructive and digital
Digital (127, 190, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 95, 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
(127, 190, 310)-Net over F3 — Digital
Digital (127, 190, 310)-net over F3, using
(127, 190, 5003)-Net in Base 3 — Upper bound on s
There is no (127, 190, 5004)-net in base 3, because
- 1 times m-reduction [i] would yield (127, 189, 5004)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1 504350 407718 759548 825240 177355 630743 437355 945881 675298 826385 290623 642545 127281 617182 918161 > 3189 [i]