Best Known (157, 258, s)-Nets in Base 4
(157, 258, 160)-Net over F4 — Constructive and digital
Digital (157, 258, 160)-net over F4, using
- 1 times m-reduction [i] based on digital (157, 259, 160)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (33, 84, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- digital (73, 175, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- digital (33, 84, 56)-net over F4, using
- (u, u+v)-construction [i] based on
(157, 258, 393)-Net over F4 — Digital
Digital (157, 258, 393)-net over F4, using
(157, 258, 8033)-Net in Base 4 — Upper bound on s
There is no (157, 258, 8034)-net in base 4, because
- 1 times m-reduction [i] would yield (157, 257, 8034)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 53746 131800 748328 015278 551661 755564 595155 159592 480312 992339 193938 396804 840104 907461 652371 112030 547315 252403 144404 429865 619066 527005 769538 343051 728361 303040 > 4257 [i]