Best Known (212−98, 212, s)-Nets in Base 4
(212−98, 212, 130)-Net over F4 — Constructive and digital
Digital (114, 212, 130)-net over F4, using
- t-expansion [i] based on digital (105, 212, 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
(212−98, 212, 194)-Net over F4 — Digital
Digital (114, 212, 194)-net over F4, using
(212−98, 212, 2524)-Net in Base 4 — Upper bound on s
There is no (114, 212, 2525)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 43 740748 174073 497451 264946 257061 776092 030012 837075 807160 096399 774377 528244 349607 333097 239055 536298 143017 648116 673568 533057 245584 > 4212 [i]