MinT - Best Known (43−27, 43, s)-Nets in Base 16

Best Known (43−27, 43, s)-Nets in Base 16

(43−27, 43, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 43, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 43, 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]

(43−27, 43, 98)-Net in Base 16 — Constructive

(16, 43, 98)-net in base 16, using

2 times m-reduction [i] based on (16, 45, 98)-net in base 16, using
- base change [i] based on digital (7, 36, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(43−27, 43, 98)-Net over F₁₆ — Digital

Digital (16, 43, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 43, 98)-net over F₁₆, using
- net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
    - a curve from the manYPoints database [i]

(43−27, 43, 2927)-Net in Base 16 — Upper bound on s

There is no (16, 43, 2928)-net in base 16, because

1 times m-reduction [i] would yield (16, 42, 2928)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 374 581838 121541 010474 148860 967523 341099 447473 150011 > 16⁴² [i]