MinT - Best Known (43, 43+83, s)-Nets in Base 16

Best Known (43, 43+83, s)-Nets in Base 16

(43, 43+83, 225)-Net over F₁₆ — Constructive and digital

Digital (43, 126, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 126, 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+83, 226)-Net over F₁₆ — Digital

Digital (43, 126, 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+83, 5022)-Net in Base 16 — Upper bound on s

There is no (43, 126, 5023)-net in base 16, because

1 times m-reduction [i] would yield (43, 125, 5023)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 274305 090637 515846 604089 468246 405209 280110 578702 646136 263646 569666 287488 520406 295697 700087 719760 267201 994560 960108 389227 008413 617955 173586 366279 979896 > 16¹²⁵ [i]