Best Known (87, 251, s)-Nets in Base 4
(87, 251, 104)-Net over F4 — Constructive and digital
Digital (87, 251, 104)-net over F4, using
- t-expansion [i] based on digital (73, 251, 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
(87, 251, 129)-Net over F4 — Digital
Digital (87, 251, 129)-net over F4, using
- t-expansion [i] based on digital (81, 251, 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
(87, 251, 661)-Net in Base 4 — Upper bound on s
There is no (87, 251, 662)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 13 147774 913971 106978 923079 268800 107510 389000 022494 470027 264385 059686 024110 051902 781877 665758 819594 993275 190988 734274 830449 675905 738025 414889 614250 603260 > 4251 [i]