Best Known (129, 129+101, s)-Nets in Base 4
(129, 129+101, 130)-Net over F4 — Constructive and digital
Digital (129, 230, 130)-net over F4, using
- t-expansion [i] based on digital (105, 230, 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+101, 245)-Net over F4 — Digital
Digital (129, 230, 245)-net over F4, using
(129, 129+101, 3674)-Net in Base 4 — Upper bound on s
There is no (129, 230, 3675)-net in base 4, because
- 1 times m-reduction [i] would yield (129, 229, 3675)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 752892 952535 223487 762499 665035 038677 940123 482587 736207 010113 773536 312011 961785 625231 219728 277048 445762 521345 896015 099514 331071 866433 488990 > 4229 [i]