MinT - Best Known (128−114, 128, s)-Nets in Base 16

Best Known (128−114, 128, s)-Nets in Base 16

(128−114, 128, 65)-Net over F₁₆ — Constructive and digital

Digital (14, 128, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 128, 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]

(128−114, 128, 97)-Net over F₁₆ — Digital

Digital (14, 128, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 128, 97)-net over F₁₆, using
- net from sequence [i] based on digital (13, 96)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 13 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(128−114, 128, 686)-Net in Base 16 — Upper bound on s

There is no (14, 128, 687)-net in base 16, because

28 times m-reduction [i] would yield (14, 100, 687)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 585219 517704 996911 697592 466527 819969 154857 798303 022739 641272 418521 930460 542750 804250 683790 033575 541092 769207 125128 290516 > 16¹⁰⁰ [i]