Best Known (257−120, 257, s)-Nets in Base 4
(257−120, 257, 130)-Net over F4 — Constructive and digital
Digital (137, 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
(257−120, 257, 223)-Net over F4 — Digital
Digital (137, 257, 223)-net over F4, using
(257−120, 257, 2881)-Net in Base 4 — Upper bound on s
There is no (137, 257, 2882)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 53663 583428 444166 194093 250532 692723 013328 199064 867277 545839 648266 557548 208080 830464 990458 810098 446098 679081 667526 637888 367775 134328 745024 574365 565873 113840 > 4257 [i]