Best Known (107, 107+64, s)-Nets in Base 4
(107, 107+64, 130)-Net over F4 — Constructive and digital
Digital (107, 171, 130)-net over F4, using
- t-expansion [i] based on digital (105, 171, 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
(107, 107+64, 320)-Net over F4 — Digital
Digital (107, 171, 320)-net over F4, using
(107, 107+64, 7004)-Net in Base 4 — Upper bound on s
There is no (107, 171, 7005)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 8 964192 205777 215931 723371 203034 803600 147833 334071 015105 170066 560937 553136 311331 699058 045995 012973 693826 > 4171 [i]