Best Known (135, 135+112, s)-Nets in Base 4
(135, 135+112, 130)-Net over F4 — Constructive and digital
Digital (135, 247, 130)-net over F4, using
- t-expansion [i] based on digital (105, 247, 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
(135, 135+112, 236)-Net over F4 — Digital
Digital (135, 247, 236)-net over F4, using
(135, 135+112, 3227)-Net in Base 4 — Upper bound on s
There is no (135, 247, 3228)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 51372 425377 433831 832153 241948 456609 456467 546135 796714 226798 961167 194432 615862 977748 876905 937945 906507 397399 241656 585962 893992 218159 096123 409087 642820 > 4247 [i]