Best Known (77, 175, s)-Nets in Base 4
(77, 175, 104)-Net over F4 — Constructive and digital
Digital (77, 175, 104)-net over F4, using
- t-expansion [i] based on digital (73, 175, 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
(77, 175, 112)-Net over F4 — Digital
Digital (77, 175, 112)-net over F4, using
- t-expansion [i] based on digital (73, 175, 112)-net over F4, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 112, using
- net from sequence [i] based on digital (73, 111)-sequence over F4, using
(77, 175, 860)-Net in Base 4 — Upper bound on s
There is no (77, 175, 861)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2334 936853 471418 127533 138988 100045 622681 809987 410495 366458 478760 180503 119816 717931 449028 475674 178581 799216 > 4175 [i]