Best Known (129, 129+113, s)-Nets in Base 4
(129, 129+113, 130)-Net over F4 — Constructive and digital
Digital (129, 242, 130)-net over F4, using
- t-expansion [i] based on digital (105, 242, 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+113, 211)-Net over F4 — Digital
Digital (129, 242, 211)-net over F4, using
(129, 129+113, 2775)-Net in Base 4 — Upper bound on s
There is no (129, 242, 2776)-net in base 4, because
- 1 times m-reduction [i] would yield (129, 241, 2776)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 12 504980 139111 054711 794912 918885 175925 822601 563745 573419 186543 817597 169356 600802 204703 505192 063475 263760 058253 894886 213177 245593 216157 852907 217480 > 4241 [i]