MinT - Best Known (30, 30+61, s)-Nets in Base 16

Best Known (30, 30+61, s)-Nets in Base 16

(30, 30+61, 65)-Net over F₁₆ — Constructive and digital

Digital (30, 91, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 91, 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]

(30, 30+61, 120)-Net in Base 16 — Constructive

(30, 91, 120)-net in base 16, using

4 times m-reduction [i] based on (30, 95, 120)-net in base 16, using
- base change [i] based on digital (11, 76, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
      - a function field by SÃ©mirat [i]

(30, 30+61, 162)-Net over F₁₆ — Digital

Digital (30, 91, 162)-net over F₁₆, using

net from sequence [i] based on digital (30, 161)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 30 and N(F) ≥ 162, using
  - a curve from the manYPoints database [i]

(30, 30+61, 3272)-Net in Base 16 — Upper bound on s

There is no (30, 91, 3273)-net in base 16, because

1 times m-reduction [i] would yield (30, 90, 3273)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 359892 336676 306896 791601 949591 231260 657245 890225 154829 836194 715622 860042 104507 889956 285203 553376 593403 626976 > 16⁹⁰ [i]