Best Known (108, 108+112, s)-Nets in Base 4
(108, 108+112, 130)-Net over F4 — Constructive and digital
Digital (108, 220, 130)-net over F4, using
- t-expansion [i] based on digital (105, 220, 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
(108, 108+112, 148)-Net over F4 — Digital
Digital (108, 220, 148)-net over F4, using
(108, 108+112, 1632)-Net in Base 4 — Upper bound on s
There is no (108, 220, 1633)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2 919066 667249 357619 316126 554323 761633 624751 820795 332907 871441 074402 279484 463373 599882 317164 581657 750905 239893 254975 694677 517490 571880 > 4220 [i]