Best Known (111, 111+68, s)-Nets in Base 4
(111, 111+68, 130)-Net over F4 — Constructive and digital
Digital (111, 179, 130)-net over F4, using
- t-expansion [i] based on digital (105, 179, 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
(111, 111+68, 316)-Net over F4 — Digital
Digital (111, 179, 316)-net over F4, using
(111, 111+68, 6640)-Net in Base 4 — Upper bound on s
There is no (111, 179, 6641)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 588240 442724 338387 707391 719391 492997 282021 819246 480628 221333 908865 063881 118218 494075 285259 382320 845951 903112 > 4179 [i]