Best Known (14, 14+110, s)-Nets in Base 16
(14, 14+110, 65)-Net over F16 — Constructive and digital
Digital (14, 124, 65)-net over F16, using
- t-expansion [i] based on digital (6, 124, 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
(14, 14+110, 97)-Net over F16 — Digital
Digital (14, 124, 97)-net over F16, using
- t-expansion [i] based on digital (13, 124, 97)-net over F16, using
- net from sequence [i] based on digital (13, 96)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 13 and N(F) ≥ 97, using
- net from sequence [i] based on digital (13, 96)-sequence over F16, using
(14, 14+110, 686)-Net in Base 16 — Upper bound on s
There is no (14, 124, 687)-net in base 16, because
- 24 times m-reduction [i] would yield (14, 100, 687)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 2 585219 517704 996911 697592 466527 819969 154857 798303 022739 641272 418521 930460 542750 804250 683790 033575 541092 769207 125128 290516 > 16100 [i]