Best Known (133, 133+69, s)-Nets in Base 3
(133, 133+69, 162)-Net over F3 — Constructive and digital
Digital (133, 202, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 101, 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
(133, 133+69, 298)-Net over F3 — Digital
Digital (133, 202, 298)-net over F3, using
(133, 133+69, 4444)-Net in Base 3 — Upper bound on s
There is no (133, 202, 4445)-net in base 3, because
- 1 times m-reduction [i] would yield (133, 201, 4445)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 799869 587773 373512 494284 238096 626498 398084 663807 778867 447570 978370 643821 953345 665999 512678 164033 > 3201 [i]