Best Known (110−84, 110, s)-Nets in Base 16
(110−84, 110, 65)-Net over F16 — Constructive and digital
Digital (26, 110, 65)-net over F16, using
- t-expansion [i] based on digital (6, 110, 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
(110−84, 110, 66)-Net in Base 16 — Constructive
(26, 110, 66)-net in base 16, using
- t-expansion [i] based on (25, 110, 66)-net in base 16, using
- net from sequence [i] based on (25, 65)-sequence in base 16, using
- base expansion [i] based on digital (50, 65)-sequence over F4, using
- t-expansion [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 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) = 49 and N(F) ≥ 66, using
- t-expansion [i] based on digital (49, 65)-sequence over F4, using
- base expansion [i] based on digital (50, 65)-sequence over F4, using
- net from sequence [i] based on (25, 65)-sequence in base 16, using
(110−84, 110, 150)-Net over F16 — Digital
Digital (26, 110, 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
(110−84, 110, 1544)-Net in Base 16 — Upper bound on s
There is no (26, 110, 1545)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 852226 750130 472821 929713 189532 333586 965584 881770 724392 588274 914500 885553 097402 630191 533830 335828 513048 372757 092571 948347 358379 934976 > 16110 [i]