Best Known (117, 117+110, s)-Nets in Base 4
(117, 117+110, 130)-Net over F4 — Constructive and digital
Digital (117, 227, 130)-net over F4, using
- t-expansion [i] based on digital (105, 227, 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
(117, 117+110, 177)-Net over F4 — Digital
Digital (117, 227, 177)-net over F4, using
(117, 117+110, 2127)-Net in Base 4 — Upper bound on s
There is no (117, 227, 2128)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 47424 810687 709640 282326 791612 155247 436323 656851 230808 258402 272219 830965 268053 791126 343022 364343 103547 815617 600331 542418 382412 071824 893444 > 4227 [i]