MinT - Best Known (30, 30+72, s)-Nets in Base 16

Best Known (30, 30+72, s)-Nets in Base 16

(30, 30+72, 65)-Net over F₁₆ — Constructive and digital

Digital (30, 102, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 102, 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+72, 104)-Net in Base 16 — Constructive

(30, 102, 104)-net in base 16, using

3 times m-reduction [i] based on (30, 105, 104)-net in base 16, using
- base change [i] based on digital (9, 84, 104)-net over F₃₂, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(30, 30+72, 162)-Net over F₁₆ — Digital

Digital (30, 102, 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+72, 2436)-Net in Base 16 — Upper bound on s

There is no (30, 102, 2437)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 664 422411 606631 203907 837206 617517 275442 979864 036323 619060 053863 176857 376247 949772 889789 403202 181126 300233 988948 334399 434356 > 16¹⁰² [i]