Best Known (194−105, 194, s)-Nets in Base 4
(194−105, 194, 104)-Net over F4 — Constructive and digital
Digital (89, 194, 104)-net over F4, using
- t-expansion [i] based on digital (73, 194, 104)-net over F4, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the 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) = 73 and N(F) ≥ 104, using
- net from sequence [i] based on digital (73, 103)-sequence over F4, using
(194−105, 194, 129)-Net over F4 — Digital
Digital (89, 194, 129)-net over F4, using
- t-expansion [i] based on digital (81, 194, 129)-net over F4, using
- net from sequence [i] based on digital (81, 128)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 81 and N(F) ≥ 129, using
- net from sequence [i] based on digital (81, 128)-sequence over F4, using
(194−105, 194, 1114)-Net in Base 4 — Upper bound on s
There is no (89, 194, 1115)-net in base 4, because
- 1 times m-reduction [i] would yield (89, 193, 1115)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 159 091667 611841 912470 894169 702565 062268 972553 063747 251330 256312 230412 653921 850884 979848 525377 014673 250074 063566 428076 > 4193 [i]