Best Known (129, 129+115, s)-Nets in Base 4
(129, 129+115, 130)-Net over F4 — Constructive and digital
Digital (129, 244, 130)-net over F4, using
- t-expansion [i] based on digital (105, 244, 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
(129, 129+115, 207)-Net over F4 — Digital
Digital (129, 244, 207)-net over F4, using
(129, 129+115, 2666)-Net in Base 4 — Upper bound on s
There is no (129, 244, 2667)-net in base 4, because
- 1 times m-reduction [i] would yield (129, 243, 2667)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 200 039694 388070 704166 953383 966542 425748 671168 246112 142052 254542 701485 840856 537776 218230 560764 741166 231667 348216 607055 136446 900469 053478 072572 617800 > 4243 [i]