Best Known (119, 119+115, s)-Nets in Base 4
(119, 119+115, 130)-Net over F4 — Constructive and digital
Digital (119, 234, 130)-net over F4, using
- t-expansion [i] based on digital (105, 234, 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
(119, 119+115, 174)-Net over F4 — Digital
Digital (119, 234, 174)-net over F4, using
(119, 119+115, 2081)-Net in Base 4 — Upper bound on s
There is no (119, 234, 2082)-net in base 4, because
- 1 times m-reduction [i] would yield (119, 233, 2082)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 194 814248 387830 635442 593248 095127 033654 895453 586331 463589 929676 252746 547555 484263 601738 205470 044858 851874 251705 014835 588695 248952 597142 073600 > 4233 [i]