Best Known (239−112, 239, s)-Nets in Base 4
(239−112, 239, 130)-Net over F4 — Constructive and digital
Digital (127, 239, 130)-net over F4, using
- t-expansion [i] based on digital (105, 239, 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
(239−112, 239, 206)-Net over F4 — Digital
Digital (127, 239, 206)-net over F4, using
(239−112, 239, 2639)-Net in Base 4 — Upper bound on s
There is no (127, 239, 2640)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 786402 090547 199077 524341 101644 834809 428998 623204 102623 210157 789175 360323 987781 441119 051447 539864 268479 716821 093138 631990 618006 242196 406241 202700 > 4239 [i]