MinT - Best Known (114−84, 114, s)-Nets in Base 16

Best Known (114−84, 114, s)-Nets in Base 16

(114−84, 114, 65)-Net over F₁₆ — Constructive and digital

Digital (30, 114, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 114, 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]

(114−84, 114, 98)-Net in Base 16 — Constructive

(30, 114, 98)-net in base 16, using

1 times m-reduction [i] based on (30, 115, 98)-net in base 16, using
- base change [i] based on digital (7, 92, 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]

(114−84, 114, 162)-Net over F₁₆ — Digital

Digital (30, 114, 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]

(114−84, 114, 2018)-Net in Base 16 — Upper bound on s

There is no (30, 114, 2019)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 187321 733779 067368 415326 515919 122841 888808 782931 378714 121451 598203 872444 437396 458799 715278 594265 000079 425227 039558 710984 929491 631291 739096 > 16¹¹⁴ [i]