Best Known (121, 121+81, s)-Nets in Base 4
(121, 121+81, 130)-Net over F4 — Constructive and digital
Digital (121, 202, 130)-net over F4, using
- t-expansion [i] based on digital (105, 202, 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
(121, 121+81, 292)-Net over F4 — Digital
Digital (121, 202, 292)-net over F4, using
(121, 121+81, 5539)-Net in Base 4 — Upper bound on s
There is no (121, 202, 5540)-net in base 4, because
- 1 times m-reduction [i] would yield (121, 201, 5540)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 10 375686 943568 990316 946006 655108 102944 026599 955562 185221 782814 699771 832965 585289 550180 219412 457646 049800 194376 459040 784400 > 4201 [i]