MinT - Best Known (43, 43+73, s)-Nets in Base 16

Best Known (43, 43+73, s)-Nets in Base 16

(43, 43+73, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 116, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 116, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(43, 43+73, 226)-Net over F₁₆ — Digital

Digital (43, 116, 226)-net over F₁₆, using

net from sequence [i] based on digital (43, 225)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 43 and N(F) ≥ 226, using
  - Drinfeld modules of rank 1 [i]

(43, 43+73, 6665)-Net in Base 16 — Upper bound on s

There is no (43, 116, 6666)-net in base 16, because

1 times m-reduction [i] would yield (43, 115, 6666)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 981749 972581 071621 610807 609647 645174 396334 254419 390999 081550 446402 395230 289667 304072 515822 509644 383903 900298 053369 199374 494294 832333 722016 > 16¹¹⁵ [i]