MinT - Best Known (103−79, 103, s)-Nets in Base 16

Best Known (103−79, 103, s)-Nets in Base 16

(103−79, 103, 65)-Net over F₁₆ — Constructive and digital

Digital (24, 103, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 103, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ 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]

(103−79, 103, 129)-Net over F₁₆ — Digital

Digital (24, 103, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 103, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(103−79, 103, 1425)-Net in Base 16 — Upper bound on s

There is no (24, 103, 1426)-net in base 16, because

1 times m-reduction [i] would yield (24, 102, 1426)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 664 254664 422808 026125 329246 957094 153056 412595 744213 365185 092304 863710 127270 284207 292281 895671 530532 172746 827792 362338 971936 > 16¹⁰² [i]