Best Known (116, 116+102, s)-Nets in Base 4
(116, 116+102, 130)-Net over F4 — Constructive and digital
Digital (116, 218, 130)-net over F4, using
- t-expansion [i] based on digital (105, 218, 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
(116, 116+102, 191)-Net over F4 — Digital
Digital (116, 218, 191)-net over F4, using
(116, 116+102, 2437)-Net in Base 4 — Upper bound on s
There is no (116, 218, 2438)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 180786 286373 876814 445205 091901 377601 341522 273458 818375 665502 509429 118402 104897 193001 513361 297991 959701 369570 552455 915223 648728 207120 > 4218 [i]