Best Known (98−72, 98, s)-Nets in Base 16
(98−72, 98, 65)-Net over F16 — Constructive and digital
Digital (26, 98, 65)-net over F16, using
- t-expansion [i] based on digital (6, 98, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(98−72, 98, 76)-Net in Base 16 — Constructive
(26, 98, 76)-net in base 16, using
- 7 times m-reduction [i] based on (26, 105, 76)-net in base 16, using
- base change [i] based on digital (5, 84, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- base change [i] based on digital (5, 84, 76)-net over F32, using
(98−72, 98, 150)-Net over F16 — Digital
Digital (26, 98, 150)-net over F16, using
- net from sequence [i] based on digital (26, 149)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 26 and N(F) ≥ 150, using
(98−72, 98, 1785)-Net in Base 16 — Upper bound on s
There is no (26, 98, 1786)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 10215 305222 604099 256290 062239 566680 392404 066110 484735 160632 666197 457590 098466 339199 656559 620840 969375 726379 280439 533066 > 1698 [i]