Best Known (136, 136+121, s)-Nets in Base 4
(136, 136+121, 130)-Net over F4 — Constructive and digital
Digital (136, 257, 130)-net over F4, using
- t-expansion [i] based on digital (105, 257, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second 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) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(136, 136+121, 217)-Net over F4 — Digital
Digital (136, 257, 217)-net over F4, using
(136, 136+121, 2815)-Net in Base 4 — Upper bound on s
There is no (136, 257, 2816)-net in base 4, because
- 1 times m-reduction [i] would yield (136, 256, 2816)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 13682 957058 417219 549438 321003 864091 690421 146858 200011 900446 863519 518011 553666 958301 425989 064794 802699 473532 776427 800930 479186 756326 784351 580292 549847 834345 > 4256 [i]