MinT - Best Known (127−94, 127, s)-Nets in Base 16

Best Known (127−94, 127, s)-Nets in Base 16

(127−94, 127, 65)-Net over F₁₆ — Constructive and digital

Digital (33, 127, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 127, 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]

(127−94, 127, 98)-Net in Base 16 — Constructive

(33, 127, 98)-net in base 16, using

3 times m-reduction [i] based on (33, 130, 98)-net in base 16, using
- base change [i] based on digital (7, 104, 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]

(127−94, 127, 193)-Net over F₁₆ — Digital

Digital (33, 127, 193)-net over F₁₆, using

net from sequence [i] based on digital (33, 192)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 33 and N(F) ≥ 193, using
  - a curve from the manYPoints database [i]

(127−94, 127, 2170)-Net in Base 16 — Upper bound on s

There is no (33, 127, 2171)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 851 454492 103634 764542 614174 573363 917583 720867 505129 532329 462132 200321 311231 265691 201564 528096 324029 404284 439040 611846 351644 404461 039297 414968 179334 788656 > 16¹²⁷ [i]