Best Known (157, 250, s)-Nets in Base 3
(157, 250, 162)-Net over F3 — Constructive and digital
Digital (157, 250, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 125, 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
(157, 250, 280)-Net over F3 — Digital
Digital (157, 250, 280)-net over F3, using
(157, 250, 3397)-Net in Base 3 — Upper bound on s
There is no (157, 250, 3398)-net in base 3, because
- 1 times m-reduction [i] would yield (157, 249, 3398)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 64175 415257 565451 697033 979816 615380 328490 224263 232664 221916 007515 376357 158087 559594 037908 456521 515295 115457 490498 950821 > 3249 [i]