MinT - Best Known (99−84, 99, s)-Nets in Base 16

Best Known (99−84, 99, s)-Nets in Base 16

(99−84, 99, 65)-Net over F₁₆ — Constructive and digital

Digital (15, 99, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 99, 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]

(99−84, 99, 98)-Net over F₁₆ — Digital

Digital (15, 99, 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]

(99−84, 99, 735)-Net in Base 16 — Upper bound on s

There is no (15, 99, 736)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 166453 292423 125804 194075 685452 223771 463337 251314 971477 373337 769445 747579 741422 125338 698282 882183 597010 285613 708122 206406 > 16⁹⁹ [i]